Question

Rosie is building a wheelchair ramp that is 12 feet long and 1.5 feet high. She needs to install a vertical support piece 4 feet from the end of the ramp. What is the length of the support piece in inches?

Answer 1

The length of the support piece is 6 inches

Solution:

The image of the problem is attached below.

Rosie is building a wheelchair ramp that is 12 feet long and 1.5 feet height.

Given, AD = 4 ft, AB = 12 ft, BC = 1.5 ft

Let us first convert feet into inches.

1 ft = 12 inches

AD = 4 ft × 12 = 48 inches

AB = 12 × 12 = 144 inches

BC = 1.5 × 12 = 18 inches

DB = AB – AD

= 144 inches – 48 inches

DB = 96 inches

ΔABC and ΔAED are similar triangles.

If two triangles are similar then their corresponding sides are in proportional.

`$(AB)/(AD) =(BC)/(DE)$`

`$(144)/(48) =(18)/(x)$`

Do cross multiplication, we get

`144* x=48*18`

Divide by 144 on both sides of the expression, we get

x = 6

The length of the support piece is 6 inches.