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 1200 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?

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 1200 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?

anonymous · Answer

attachment

phi · Answer

first step,  the 2 triangles are congruent. Do you know why?

anonymous · Answer

Yes.. because of the slashes. What I figured was... the 30 degrees is the height and the area for triangle is a=1/2bh since my area is 1200 I said 1200=1/2b(30) and figured the bass was 80. So my answer is 80? is thst right?

phi · Answer

sounds good.  the "right answer" for congruent is side - angle -side  (the angle has to be equal, which it is)
so both have the same altitude = 30  and same base
so A= 1200 = 1/2 b*30
b= 1200/15= 80

congruent means that b is the same for both.  80 is the answer