SOLUTION: The lone base of a trapezoid is twice the length of the short base. If the height is 16 yards and the area is 336 square yards, what is the perimeter of the trapezoid?

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Question 744774: The lone base of a trapezoid is twice the length of the short base. If the height is 16 yards and the area is 336 square yards, what is the perimeter of the trapezoid?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The length of the bases may be m and 2m. If you draw a trapezoid with one leg making right angles with each base, then this leg is also a height.

Area 336=16%2A%28m%2B2m%29%2F2
16%2A3m%2F2=336
8%2A3m=336
m=336%2F24
m=14 and then 2m=28

Now if you have drawn this, the other leg is the hypotenuse of a right triangle. The base of this triangle may be seen as m and the height is again 16. The hypotenuse can be found. h is hypotenuse, this other leg, h%5E2=14%5E2%2B16%5E2.

The perimeter of the trapezoid is +m+%2B+2m+%2B+16+%2B+h+=+3%2A14%2B16%2Bh


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h=2sqrt%28113%29, so perimeter is 58%2B2%2Asqrt%28113%29