At the outside wall the roof is 9 feet high. Also, 5 horizontal feet from the outside wall to- ward the interior of the room, the roof is 10 feet tall. If the roof is extended beyond the outside wall, what is
The height of the roof 4 horizontal feet from the outside wall toward the exterior of the room?
A) 9.15 feet
B) 7 feet
C) 8.2 feet
D) 7.14 feet

Question

Quizplus · Accepted Answer

We can use similar triangles to solve the problem. Let x be the height of the roof 4 horizontal feet from the outside wall toward the exterior of the room. Then, we have two similar right triangles:

- The first triangle has legs 9 feet and 5 horizontal feet, and a hypotenuse of 10 feet.
- The second triangle has legs x and 4 horizontal feet, and a hypotenuse that extends beyond the outside wall.

Since the triangles are similar, we can set up the following proportion:

9/5 = 10/x

Solving for x, we get:

x = 45/9 = 5

Therefore, the height of the roof 4 horizontal feet from the outside wall toward the exterior of the room is 5 feet.

At the Outside Wall the Roof Is 9 Feet High