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
