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 QR measures 6x + 4. Find the value of x

For this problem, we can set up a proportion using similarity ratios. We know that triangle DEF is similar to triangle PQR, so we know that DE/PQ = EF/QR = FD/RP:

DE/PQ = EF/QR

3 / (5x - 25) = 7 / (6x + 4)

Cross multiplying, we get:

7 (5x - 25) = 3 (6x + 4)

35x - 175 = 18x + 12

Now, we can solve for x:

35x - 18x = 12 + 175

17x = 187

x = 11

So, x is 11.