Camila needs to fix the window on the front of her house. The bottom of the window is 16 ft. from the ground. She only has a 20 ft. ladder. How far from the base of the house should she set up the ladder so that the top of the ladder is exactly at the bottom of the window? not 4ft
To determine the distance from the base of the house where Camila should set up the ladder, we need to find the distance from the top of the ladder to the bottom of the window.
Since the bottom of the window is 16 ft. from the ground, and Camila has a 20 ft. ladder, the top of the ladder should be 16 ft. + 20 ft. = <<16+20=36>>36 ft. from the ground.
Therefore, Camila should set up the ladder 36 ft. from the base of the house.
wrong
I apologize for the incorrect response.
To determine the distance from the base of the house where Camila should set up the ladder, we need to subtract the height of the ladder (20 ft.) from the height of the window sill (16 ft.).
16 ft. - 20 ft. = -4 ft.
Since it's not possible to set up the ladder at a negative distance from the base of the house, Camila cannot use the 20 ft. ladder to fix the window. She would require a taller ladder or find an alternative solution.
try again
Apologies for the confusion. Let's try again.
To determine the distance from the base of the house where Camila should set up the ladder, we need to subtract the height of the window from the length of the ladder.
If the bottom of the window is 16 ft. from the ground and the ladder is 20 ft. long, we need to subtract 16 ft. from 20 ft. to find the distance from the base of the house where Camila should set up the ladder.
20 ft. - 16 ft. = 4 ft.
Therefore, Camila should set up the ladder 4 ft. from the base of the house so that the top of the ladder is exactly at the bottom of the window.
nope try agian Camila needs to fix the window on the front of her house. The bottom of the window is 16 ft. from the ground. She only has a 20 ft. ladder. How far from the base of the house should she set up the ladder so that the top of the ladder is exactly at the bottom of the window?
Apologies for the previous incorrect response. Let's try again.
To determine how far from the base of the house Camila should set up the ladder, we need to find the vertical distance from the ground to the bottom of the window and subtract that from the height of the ladder.
Given that the bottom of the window is 16 ft. from the ground and Camila has a 20 ft. ladder, we need to subtract 16 ft. from 20 ft. to find the distance.
20 ft. - 16 ft. = 4 ft.
Therefore, Camila should set up the ladder 4 ft. from the base of the house so that the top of the ladder is exactly at the bottom of the window.
use the pythagorean theorem
Apologies once again. Let's use the Pythagorean theorem to find the correct distance.
In this case, the distance from the base of the house where Camila should set up the ladder can be found using the Pythagorean theorem, which states that for a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this scenario, the ladder acts as the hypotenuse, the distance from the base of the house to the ladder's placement acts as one side, and the height from the ground to the bottom of the window acts as the other side.
Let's denote the distance from the base of the house to the ladder's placement as x.
Applying the Pythagorean theorem, we have:
x^2 + 16^2 = 20^2
Simplifying this equation:
x^2 + 256 = 400
Subtracting 256 from both sides:
x^2 = 400 - 256
x^2 = 144
Taking the square root of both sides gives us:
x = √144
x = 12
Therefore, Camila should set up the ladder 12 ft. from the base of the house so that the top of the ladder is exactly at the bottom of the window.
Use the image to answer the question.
A rectangle is formed from two right triangles. The base of the rectangle measures 80 yards and is labeled Johnson Avenue. The top of the rectangle is labeled Edison Avenue. The left side joining both the avenues is labeled 41st street and measures 60 yards. The right side of the rectangle is labeled 42nd street. A bank is located at the vertex of 41st street and Edison Avenue. The hypotenuse joining the bank and the vertex of Johnson Avenue and 42nd street is labeled park.
Sylvia likes to walk to work when the weather is nice. She works at the bank at the corner of 41st Street and Edison Avenue. Her house is at the corner of 42nd Street and Johnson Avenue. She can walk down Johnson Avenue and turn right on 41st Street, or she can walk through the park. The distance from 42nd Street to 41st Street is 80 yards, and it is 60 yards from Johnson Avenue to Edison Avenue. Assuming the street intersections are 90° angles, how much shorter is it for Sylvia to walk through the park?
(1 point)
If Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be
yards shorter.use the pythagorean theorem
To find out how much shorter it is for Sylvia to walk through the park, we can use the Pythagorean theorem.
Given:
- The base of the rectangle (Johnson Avenue) measures 80 yards.
- The left side of the rectangle (41st Street) measures 60 yards.
We can consider the hypotenuse of the right triangle formed by these sides as the distance Sylvia needs to walk if she goes through the park.
Using the Pythagorean theorem, we can find the length of this hypotenuse:
a^2 + b^2 = c^2
where:
a = 80 yards
b = 60 yards
c = distance through the park (hypotenuse)
Plugging in the values:
80^2 + 60^2 = c^2
6400 + 3600 = c^2
10000 = c^2
Taking the square root of both sides to find c:
√10000 = c
c = 100 yards
Therefore, if Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, her walk will be 100 - 80 = 20 yards shorter.
try agian
Apologies for the incorrect response. Let's try again.
To determine how much shorter it is for Sylvia to walk through the park, we can compare the two possible paths using the Pythagorean theorem.
The distance from Sylvia's house to the bank can be found by calculating the hypotenuse of the right triangle formed by Johnson Avenue (80 yards) and 42nd Street (60 yards).
Using the Pythagorean theorem:
a^2 + b^2 = c^2
where:
a = length of Johnson Avenue = 80 yards
b = length of 42nd Street = 60 yards
c = hypotenuse (distance from Sylvia's house to the bank)
Plugging in the values:
80^2 + 60^2 = c^2
6400 + 3600 = c^2
10000 = c^2
Taking the square root of both sides to find c:
√10000 = c
c = 100 yards
So, the distance from Sylvia's house to the bank walking along the streets is 100 yards.
On the other hand, if Sylvia walks through the park, the distance she needs to travel is the same as the hypotenuse of the right triangle formed by 41st Street (60 yards) and Edison Avenue (80 yards).
Using the Pythagorean theorem again:
a^2 + b^2 = c^2
where:
a = length of 41st Street = 60 yards
b = length of Edison Avenue = 80 yards
c = hypotenuse (distance through the park)
Plugging in the values:
60^2 + 80^2 = c^2
3600 + 6400 = c^2
10000 = c^2
Taking the square root of both sides to find c:
√10000 = c
c = 100 yards
So, the distance from Sylvia's house to the bank walking through the park is also 100 yards.
Therefore, the distance is the same whether Sylvia walks through the streets or through the park. There is no difference in distance.
nope
Apologies once again for the incorrect response. Let's try solving the problem correctly.
To determine how much shorter it is for Sylvia to walk through the park, we need to compare the two paths using the Pythagorean theorem.
The distance from Sylvia's house to the bank can be found by calculating the length of the hypotenuse of the right triangle formed by Johnson Avenue (80 yards) and 42nd Street (60 yards).
Using the Pythagorean theorem:
a^2 + b^2 = c^2
where:
a = length of Johnson Avenue = 80 yards
b = length of 42nd Street = 60 yards
c = length of the hypotenuse (distance from Sylvia's house to the bank)
Plugging in the values:
80^2 + 60^2 = c^2
6400 + 3600 = c^2
10000 = c^2
Taking the square root of both sides to find c:
√10000 = c
c = 100 yards
Therefore, if Sylvia walks straight down Johnson Avenue and then straight down 42nd Street, the total distance she needs to walk is 100 yards.
Now, let's consider the path through the park. Since the park is a direct path from Sylvia's house to the bank, it acts as a straight line.
Therefore, the distance through the park is simply the length of the diagonal of the rectangle formed by 41st Street (60 yards) and Edison Avenue (80 yards).
Using the Pythagorean theorem:
a^2 + b^2 = c^2
where:
a = length of 41st Street = 60 yards
b = length of Edison Avenue = 80 yards
c = diagonal length of the rectangle (distance through the park)
Plugging in the values:
60^2 + 80^2 = c^2
3600 + 6400 = c^2
10000 = c^2
Taking the square root of both sides to find c:
√10000 = c
c = 100 yards
Therefore, if Sylvia walks through the park, the total distance she needs to walk is also 100 yards.
In conclusion, whether Sylvia walks through the streets or through the park, the distance she needs to travel is the same – 100 yards.
wrong
Apologies for the repeated incorrect responses. Let's attempt to solve the problem correctly this time.
To find out how much shorter it is for Sylvia to walk through the park, we need to calculate the length of both paths separately and then compare them.
Path 1: Walking through the streets
- Straight down Johnson Avenue: 80 yards
- Right turn onto 41st Street: 60 yards
Path 2: Walking through the park (hypotenuse)
- Distance between the vertex of 41st Street and Edison Avenue (base of the rectangle): 80 yards
- Distance between Johnson Avenue and 42nd Street (side of the rectangle): 60 yards
We can use the Pythagorean theorem to find the length of the diagonal (hypotenuse):
a^2 + b^2 = c^2
where:
a = 80 yards
b = 60 yards
c = length of the hypotenuse (park path)
Plugging in the values:
80^2 + 60^2 = c^2
6400 + 3600 = c^2
10000 = c^2
Taking the square root of both sides to find c:
√10000 = c
c = 100 yards
Therefore, the length of the path through the park is 100 yards.
To find out how much shorter the park path is compared to walking through the streets, we subtract the length of the park path from the length of the street path:
Length of street path - Length of park path
= (80 + 60) - 100
= 140 - 100
= 40 yards
Therefore, it is 40 yards shorter for Sylvia to walk through the park compared to walking straight down Johnson Avenue and turning onto 41st Street.