Question

The picture below shows the location of Tim, Kathy, Joe, and Brenda’s houses near a community hall. The shaded triangle has an area of 400 square feet. The road connecting Tim and Brenda’s houses is bisected by the road connecting Joe and Kathy’s houses, as shown below.
What is the length of the road between Joe and Brenda’s houses?

Answer 1

@Hero

Answer 2

@Hero

Answer 3

@phi

Answer 4

I think the 40 ft at the bottom is the distance from the community center to road between Joe and Brenda. That is the altitude of the triangle.

the two triangles are congruent (by side-side-side)
so both have area = 400 sq ft

Area = 1/2 base* altitude
400 = 1/2 base * 40

solve for base (= distance between Joe and Brenda)

Answer 5

20?

Answer 6

@phi

Answer 7

yes

Answer 8

so the answer is 20? @phi

Answer 9

yes

Answer 10

Thank you so much! @phi

Answer 11

yw