Question

a gardener wants to create a rectangular vegetable garden in a backyard. She wants to have a total area of 108 square feet, and it should be 12 feet longer than it is wide. What dimensions should she use for the vegetable garden?

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Answer 1

Step-by-step explanation:

Let W=width of the garden.

Then length of the garden is W+12.

Area of the garden = W(W+12) = 108.....................(1)

rearrange (1)

W^2+12W-108 = 0...................(2)

Factor (2) [ 108 = 3^3*2^2 = 8*12 = 6*18 = ...]

W^2+12W-108 = W^2+18W - 6W -6*18 = W(W+18)-6(W-18) = (W+18)(W-6) = 0

Therefore W=-18, or W=6.

Rejecting negative roots, W=6, therefore length, L = 6+12 = 18

Answer: The garden measures 18' by 6'.