Answer:
x = 13
Step-by-step explanation:
BD is the hypotenuse of the smaller triangle and corresponds to 2x - 7. 51 is the longer leg of triangle EFG
The ratio of the two hypotenuses is (2x - 7)/57, and the ratio of the two longer legs is (x + 4)/51. These ratios are equal to one another. Thus:
2x - 7 x + 4
--------- = ---------
57 51
Cross multiplication results in 51(2x - 7) = 57x + 228, or
102x - 357 = 57x + 228
Combining like terms, we get:
45x = 585, and so x = 13.
