SOLUTION: The area of an isosceles trapezoid is 45 cm2 and its height is 5 cm. Find the perimeter if one of the legs is 2/3 of the sum of the bases.

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Question 1028931: The area of an isosceles trapezoid is 45 cm2 and its height is 5 cm. Find the perimeter if one of the legs is 2/3 of the sum of the bases.
Answer by MathTherapy(10557) About Me  (Show Source):
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The area of an isosceles trapezoid is 45 cm2 and its height is 5 cm. Find the perimeter if one of the legs is 2/3 of the sum of the bases.
Area = %28b%5B1%5D+%2B+b%5B2%5D%29%2F2+%2A+h, where: matrix%281%2C9%2C+b%5B1%5D%2C+and%2C+b%5B2%5D%2C+are%2C+base%2C+1%2C+and%2C+base%2C+2%29, and h = height

45+=+%28b%5B1%5D+%2B+b%5B2%5D%29%2F2+%2A+5 ------- Substituting 45 for area; and 5 for h (height)

9+=+%28b%5B1%5D+%2B+b%5B2%5D%29%2F2 ---------- Dividing numerators by 5

b%5B1%5D+%2B+b%5B2%5D+=+18 ----------- Cross-multiplying



Since one leg is 2%2F3 the sum of the bases, then we can say that one leg (L) = %282%2F3%29+%2A+%28b%5B1%5D+%2B+b%5B2%5D%29

L+=+%282%2F3%29+%2A+18 ------- Substituting 18 for b%5B1%5D+%2B+b%5B2%5D

L, or one of the legs = 12 units



Perimeter of isosceles trapezoid:  = 18 + 2(12), or 18 + 24, or highlight_green%28matrix%281%2C2%2C+42%2C+units%29%29