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?
(1 point)
She should set up the ladder 4 ft. from the base of the house.
To determine the distance from the base of the house where Camila should set up the ladder, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the ladder is the hypotenuse, the distance from the base of the house to the ladder is one side, and the distance from the base of the house to the bottom of the window is the other side.
Let's call the distance from the base of the house to the ladder x. So we have:
x^2 + 16^2 = 20^2
Simplifying, we get:
x^2 + 256 = 400
Subtracting 256 from both sides:
x^2 = 144
Taking the square root of both sides:
x = 12
Therefore, Camila should set up the ladder 12 ft. from the base of the house.
To solve this problem, we can use the concept of similar triangles.
Let's say that the distance from the base of the ladder to the house is 'x'. According to the information given, the height of the window is 16 ft and the ladder height is 20 ft.
Since the top of the ladder should be at the bottom of the window, the ladder height will be equal to the distance from the ground to the window. So, the ladder height is also 16 ft.
Now, we can set up a proportion using the similar triangles:
x/20 = 16/16
Simplifying the proportion, we get:
x/20 = 1
To solve for 'x', we can cross multiply:
x = 20
Therefore, Camila should set up the ladder 20 ft from the base of the house to ensure that the top of the ladder is exactly at the bottom of the window.
Wrong
You are right, I apologize for the error in my response.
To determine the distance from the base of the house where Camila should set up the ladder, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's call the distance from the base of the house to the ladder x. So we have:
x^2 + 16^2 = 20^2
x^2 + 256 = 400
Subtracting 256 from both sides:
x^2 = 144
Taking the square root of both sides:
x = 12
Therefore, Camila should set up the ladder 12 ft from the base of the house.