ryan is 5 feet tall. his shadow is 9 feet long and the shadow of a building is 36 feet long. how tall is the building?
5/9 = x/36
Cross multiply and solve for x.
x=20ft
To find the height of the building, we can use the concept of similar triangles. The ratio of the height of a person to the length of their shadow is equal to the ratio of the height of the building to the length of its shadow.
Given that Ryan is 5 feet tall and his shadow is 9 feet long, we have:
Ryan's height = 5 feet
Ryan's shadow = 9 feet
Let's denote the height of the building as "x" and the length of the building's shadow as "y". We know that Ryan's height to shadow ratio is the same as the building's height to shadow ratio:
5 / 9 = x / y
Now we can solve for the height of the building (x). By cross-multiplying, we get:
5y = 9x
Since the shadow of the building is 36 feet long, we can substitute this value for "y" in the equation:
5 * 36 = 9x
180 = 9x
Dividing both sides of the equation by 9:
x = 180 / 9
x = 20
Therefore, the height of the building is 20 feet.
To determine the height of the building, we can use the concept of similar triangles.
Similar triangles have proportional sides, meaning that corresponding sides are in the same ratio. In this case, we can compare the ratio of Ryan's height to his shadow with the ratio of the building's height to its shadow.
Let H represent the height of the building. We are given that Ryan's height (5 feet) corresponds to a shadow length of 9 feet. Similarly, the building's height (H) corresponds to a shadow length of 36 feet.
Using the concept of similar triangles, we can set up a proportion:
Ryan's height / Ryan's shadow = Building's height / Building's shadow
5 / 9 = H / 36
To solve for H, we cross-multiply:
5 * 36 = 9 * H
180 = 9H
Dividing both sides by 9:
H = 180 / 9
Hence, the height of the building is 20 feet.