SOLUTION: One base of a trapezoid measures 5 cm. more than the other while the altitude is 4/3 times as long as the shorter base. Find the lenghts of the bases if the area is 100 cm².

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Question 243265: One base of a trapezoid measures 5 cm. more than the other while the altitude is 4/3 times as long as the shorter base. Find the lenghts of the bases if the area is 100 cm².
Answer by kamaldas(6) About Me  (Show Source):
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Area of a trapezoid = 1/2 *(base1 +base2) * altitude
Lets assume shorter base = b
Given:
Longer base = b+5
Altitude = 4/3 b
Area = 100
Area of a trapezoid = 1/2 *(base1 +base2) * altitude
100 = 1/2 * (b+b+5) * 4/3 b
100 = 2/3 * (2 b +5) * b
Multiplying both sides by 3
300 = 2 * (2 b +5) * b
300 = 4b^2 + 10b
4b^2 +10b -300 =0
2b^2 +5b -150 =0
Factoring
(2b - 15) (b +10)=0
or b = 15/2 or -10
As distance is not negative
b =15/2 or 7.5 cm
Shorter base = 7.5 cm
Longer base = 7.5+5 =12.5 cm
Altitude = 4/3 *7.5 =10 cm