A 19 in. monitor has a length of 16 in. What is its width?
10.247 in.
14.645 in.
16.512 in.
18.918 in.
To find the width of the monitor, we can use the Pythagorean theorem.
The Pythagorean 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 monitor can be seen as a right triangle, with the length as one side and the width as the other side.
Let's denote the width as "w".
According to the Pythagorean theorem, we have:
(16)^2 + w^2 = (19)^2
Simplifying the equation, we get:
256 + w^2 = 361
Subtracting 256 from both sides, we have:
w^2 = 361 - 256
w^2 = 105
Taking the square root of both sides, we get:
w = √105
Using a calculator, we find that √105 ≈ 10.247.
Therefore, the width of the monitor is approximately 10.247 inches.
The closest answer choice is 10.247 in.
A tree 8 m tall casts a shadow of 15 m long on the ground. Find the distance between the top of the tree and the end of its shadow.
23 m
12.7 m
7 m
17 m
We can solve this problem using similar triangles and the concept of proportional reasoning.
Let's denote the distance between the top of the tree and the end of its shadow as "x".
The height of the tree, the length of the shadow, and the distance between the top of the tree and the end of its shadow form a right triangle.
Using the concept of similar triangles, we can write the following proportion:
(height of the tree) / (length of shadow) = x / (length of shadow + x)
Substituting the given values, we have:
8 / 15 = x / (15 + x)
Cross-multiplying the proportion, we get:
8(15 + x) = 15x
Simplifying the equation, we have:
120 + 8x = 15x
Subtracting 8x from both sides, we get:
120 = 7x
Dividing both sides by 7, we have:
17.14 = x
Therefore, the distance between the top of the tree and the end of its shadow is approximately 17.14 meters.
The closest answer choice is 17 m.
How far up a wall will a 11 m ladder reach if the foot of the ladder is 4 m from the base of the wall?
10.25 m
11.7 m
7 m
15 m
We can solve this problem using the Pythagorean theorem.
Let's denote the height up the wall that the ladder will reach as "h".
According to the Pythagorean theorem, we have:
(foot of the ladder)^2 + h^2 = (length of the ladder)^2
Substituting the given values, we have:
(4)^2 + h^2 = (11)^2
16 + h^2 = 121
Subtracting 16 from both sides, we have:
h^2 = 121 - 16
h^2 = 105
Taking the square root of both sides, we get:
h ≈ √105
Using a calculator, we find that √105 ≈ 10.247.
Therefore, the ladder will reach approximately 10.247 meters up the wall.
The closest answer choice is 10.25 m.
To find the width of the 19 in. monitor, we can set up a proportion using the given length and width.
Let's denote the width of the monitor as 'x'.
The proportion can be set up as:
Width / Length = Monitor Size / Given Monitor Length
x / 16 = 19 / 19
Cross-multiplying, we get:
19x = 16 * 19
Simplifying:
19x = 304
To solve for 'x', we divide both sides of the equation by 19:
x = 304 / 19
Calculating the division:
x = 16
Therefore, the width of the 19 in. monitor is 16 in.
To find the width of the monitor, we can use the formula for the aspect ratio of a monitor:
Aspect Ratio = Width / Height
In this case, the height is given as 19 inches and the length is given as 16 inches. We want to find the width.
Rearranging the formula, we can solve for the width:
Width = Aspect Ratio × Height
The aspect ratio is usually given as a ratio of width to height, such as 16:9 or 4:3. However, in this case, the aspect ratio is not provided.
Therefore, without knowing the aspect ratio, we cannot accurately determine the width of the 19-inch monitor based solely on the given information.