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] The area of trapezoid TRAP is 100. Furthermore, TR = 32, AP = 8, and TP = RA. If ∠T = ∠R, what is the length of segment TP?

 May 19, 2023
 #1
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Let H be the foot of the perpendicular from T to RA. Since T and R are congruent angles, triangles THP and RHA are congruent, so PH=HA=1/2*​AP=4. The area of trapezoid TRAP is 1/2*(TR+AP)(PH+HA)=1/2*​(32+8)(4+4)=100, so TP=RA=10​.

 May 19, 2023
 #2
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Hello! I'm not sure if me or the other person is correct but I got 5 as my answer. 

 

20*h= 100

h = 100/20 = 5

 

To check the answer:

32+8=40/2=20*5=100

 

Therefore I think the answer is 5.

 May 20, 2023

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