Hi so this is how you solve it:
We let the width of the swimming pool be x, this would make the length be x + 8 since it is 8m longer than the width.
So:
Area = length * width
105m² = (x+8)m*(x)m
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 a difference of 8 so:
105 - 1 = 104 X
35 - 3 = 32 X
21 - 5 = 16 X
15 - 7 = 8 √
So,
0 = x² + 8x - 105
0 = (x-7)(x+15)
We equate each to zero (since one factor needs to be zero in order for the product to be zero)
If (x-7) = 0 If (x+15) = 0
x = 7 x = -15
We cannot have a negative length so the width is equal to 7m and the length is equal to 15m.
Method 2: Quadratic Formula
x² + 8x - 105.
x= -8 ± √(8²+420) = -8 ± √(64+420) = -8 ± √484 = -8 ± 22 = 7 or -15
2 2 2 2
So then again, a length cannot be negative so the width is equal to 7m and the length is equal to 15m.
