Problem 47)
Find the hypotenuse of the larger triangle. Use the pythagorean theorem
a^2 + b^2 = c^2
5^2 + 12^2 = c^2
169 = c^2
c^2 = 169
c = sqrt(169)
c = 13
The two segments of 12x and 14x add up to this 13 unit long hypotenuse
So,
12x+14x = 13
26x = 13
26x/26 = 13/26
x = 1/2
Answer is choice E) 1/2
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Problem 48)
This one is a bit tricky. P1 and P2 are known
P1 = -2
P2 = -1
P3,P4,P5 are unknown. But it looks like maybe P3 = 0.25, P4 = 0.75, P5 = 1.5 or roughly close to it
So,
P1*P2*P3*P4*P5 = (-2)*(-1)*0.25*0.75*1.5 = 0.5625 which is closest to 2/3 = 0.67
Answer is B) 2/3
