Question

A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height, and the longer base to be 7 yards greater than the height. the total area of the flower garden is 150 square yards. what will the length of each base be

Answer 1

From your information 
Let shorter base = h +3 and longer base = h + 7 where h is the height.
Formula for area of a trapezoid is $A = \frac{1}{2} (b_1 +b_2)h$
Substituting into the formula we get the following equation.
$150= \frac{1}{2}(h+3+h+7)h$
$150 = \frac{1}{2} (2h+10)h$
$150=h^2+5h$
This is a quadratic equation which I will solve by factoring.
$h^2+5h-150 =0$
$(h-10)(h+15)=0$
$h-10= 0 ..... h=10$ this is a useable answer (it's positive and length must be nonnegative)
$h+15=0 .... h=-15$ can't use this answer
so shorter base = 10 + 3 = 13 yards and longer base = 10 + 7 = 17 yards