triangle DEF is similar to triangle PQR. side DE measures 3. side EF measures 7 and side FD measures 9. side PQ measures 5x-25 and side RP measures 10x-5. find x

Question

anonymous · Answer

Your question is unclear, so I will solve for everything.



The ratio of DE to FD is equal to the ratio of PQ to RP:
3 / 9 = 5x-25 / 10x-5

3(10x-5) = 9(5x-25)
30x - 15 = 45x - 225
30x + 210 = 45x
210 = 15x
14 = x

Plug in x in the expressions for the sides:
5x-25 = 5(14) - 25 = 70 - 25 = 45
10x - 5 = 10(14) - 5 = 140 - 5 = 135

Use the following proportion to solve for side QR:
EF/FD = QR/RP
7 / 9 = QR / 135
9(QR) = 135(7)
QR = 15(7)
QR = 105

To sum up:
DE = 3
EF = 7
FD = 9
PQ = 45
QR = 105
RP = 135
x = 14