Answer:
Length = 22, Width = 16
Explanation:
Let L be the length of the garden and W the width
The area, A = L x W = 352 ft²
It is given that L = W + 6
Substituting for L in the area equation we get
L x W
==> (W + 6) x W = 352
Expanding the brackets
==> W.W + 6.W = 352
==> W² + 6W = 352
Subtract 352 from both sides:
W² + 6W - 352 = 0
This is a quadratic equation which can be solved using the quadratic formula.
- 352 = - 16 x 22 and -16 + 22 = 6
So we can factor the quadratic equation as
(W - 16) (W + 22) = 0
==> W = 16 or W = -22
Since we can disregard negative values in this context,
W = 16 and L = W + 6 = 16 + 6 = 22
Dimensions are Length = 22, Width = 16