A = (1/2) b * h
h = b - 5
42 = (1/2) * b * (b - 5)
42 = (1/2) * b^2 - 5b
multiply both sides by 2 to clear the fraction (1/2)
2(42) = 2(1/2) *b^2 - 5b
84 = b^2 -5b
Since this is a quadratic equation, subtract 84 from both sides so that it is set = to zero.
b^2 - 5b - 84 = 0
Now factor.
(b - 12)(b + 5) = 0
b - 12 = 0; b = 12
b + 5 = 0; b = -5
You can't have a negative length so the answer is 12m
To check the answer:
A = (1/2) * 12* 7
A = 42 m^2
