# 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?

##### 1 Answer

Nov 21, 2016

The height is

#### Explanation:

Let the height be

#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

Hopefully this helps!