Question

In a trapezoid, the smaller base is 3 more than the height, the larger base is 5 less than 3 times the height, and the area of the trapezoid 45 square centimeters. How do you find, in centimeters, the height of the trapezoid?

Answer 1

The height is `5` cm.

Explanation:

Let the height be `x`, the smaller base be `x + 3` and the larger base be `3x - 5`. Recall the area of a trapezoid is given by `A = ((b_1 + b_2)h)/2`, where `b_1` and `b_2` are the two bases.

`45 = ((x + 3 + 3x - 5)x)/2`

`90 = (4x - 2)x`

`90 = 4x^2 - 2x`

`0 = 4x^2 - 2x - 90`

`0 = 2(2x^2 - x - 45)`

`0 = 2x^2 - 10x + 9x - 45`

`0 = 2x(x -5) + 9(x- 5)`

`0 = (2x + 9)(x - 5)`

`x = -9/2 and 5`

A negative answer is impossible, so the height of the trapezoid is `5` cm.

Hopefully this helps!