SOLUTION: The area of a trapezoid is 77 square inches, the height measures 4 inches and the legs are 5 inches long. Find the length of the bases.

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Question 954845: The area of a trapezoid is 77 square inches, the height measures 4 inches and the legs are 5 inches long. Find the length of the bases.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
With height 4in and legs 5in, a 3-4-5 triangle is formed,
with the third side (3 in) being how much longer one base is
than the other on each end. So one base is 6 inches longer.
a=shorter base; b=longer base=a+6in; h=height=4in; A=Area=77 sq in
A=%28%28a%2Bb%29%2F2%29h Substitute for b
A=%28%28a%2B%28a%2B6in%29%29%2F2%29h
77in%5E2=%28%282a%2B6in%29%2F2%294in
77in%5E2=%28a%2B3in%294in
77in%5E2=4in%28a%29%2B12in%5E2 Subtract 12in%5E2 from each side
65in%5E2=4in%28a%29 Divide each side by 4in
16.25in=a ANSWER 1: The shorter base is 16.25 inches.
a%2B6in=16.25%2B6in=22.25in ANSWER 2: The longer base is 22.25 inches.
CHECK:
A=%28%28a%2Bb%29%2F2%29h
77in%5E2=%28%2816.25in%2B22.25%29%2F2%294in
77in%5E2=%28%2838.5in%2F2%294in%29
77in%5E2=%2819.25in%294in
77in%5E2=77in%5E2