Answer:
Step-by-step explanation:
I'll answer the question, but before I do, let me crab about the reliance on a diagram. You should never have to answer a question where you make assumptions about the diagram. It should state the the longest leg in one triangle = 2x - 4, and the hypotenuse in the larger triangle is 42, while in the smaller one it is x + 8\
Added to which you have to state that there is a ratio between the large triangle and the small one.
24/(2x - 4) = (x + 8)/42 Cross Multiply
24*42 = (x + 8)*(2x - 4) Remove the brackets. Combine the left
1008 = 2x^2 - 4x + 16x - 32 Combine the right and switch
2x^2 + 12x - 32 = 1008 Subtract 1008
2x^2 + 12x - 1040 = 0 Divide by 2
x^2 + 6x - 520 = 0
(x + 26)(x - 20) = 0
x = - 26 which has no meaning
x = 20 which is the answer.
2x - 4 = 2*20 - 4 = 36
x + 8 = 28
I'm not sure what you want -- the side lengths or just x.
