We let the width be x, this would make the length x+8 so:
Area = length * width
105 = (x+8)x
105 = x²+8x
0 = x²+8x-105
Method 1: Guess and Check
We look for two numbers with a product of 105 and an absolute difference of 8.
105 - 1 = 104 X
35 - 3 = 32 X
21 - 5 = 16 X
15 - 7 = 8 √
Therefore:
0 = (x+15)(x-7)
So the possible value of x are -15 and 7. We cannot have a negative value since a length is never negative.
Method 2: Quadratic Formula
x = -8 ± √(8²+420) = -8 ± √484 = -8 ± 22 = -15 or 7
2 2 2
Again we cannot have a negative length so we only consider 7.
So the width is 7m and the length is 15m.
