Posted by **Beatrice** on Wednesday, January 4, 2012 at 3:30pm.

The area of a trapezoid is 66 sq units. The length of its longer base is 4 units longer than the length of its shorter base, and its height is 7 units longer than the length of its shorter base. Find the length of each base and the height of the trapezoid.

- Math -
**Steve**, Wednesday, January 4, 2012 at 4:26pm
you know that with bases b and c, and height h, a trapezoid has area

a = h * (b+c)/2

Just plug in your numbers, letting x be the length of the short base:

a = (x+7) * (x + x+4)/2

66 = (x+7)(x+2)

x^2 + 9x - 52 = 0

(x+13)(x-4) = 0

x = 4

short base = 4

long base = 8

height = 11

area = 11(8+4)/2 = 11*6 = 66

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