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 is 45 square centimeters. find the height in centimeters. use an algebraic solution.

The area of a trapezoid is the average of the bases times the height...

A=h(b1+b2)/2

2A=h(b1+b2)

h=(2A)/(b1+b2)

b1=h+3, b2=3h-5, A=45 so

h=(2*45)/(h+3+3h-5)

h=90/(4h-2)

4h^2-2h=90

4h^2-2h-90=0

2(2h^2-h-45)=0

2(2h^2-10h+9h-45)=0

2(2h(h-5)+9(h-5)=0

2(2h+9)(h-5)=0  since h>0

h=5 cm