A walkway xfeet wide is around a 40 ft by 30 ft garden.Area of walkway is 984 ft²What is width of the walkway?

Question

I know the answer is 12 ft because I solved it by guess and check, but how would you solve it algebraically?

Answer 1

My answer is x = 6 ft. Area of the walkway is the difference between the area determined by the outer perimeter of the walkway and the area of the enclosed garden.

Area of the enclosed garden = 30 * 40 =1,200

Area determined by the outer perimeter of the walkway = (30+2x) * (40+2x)

Need:

(30+2x) * (40+2x) - 1,200 = 984

1,200 + 80x + 60x + 4x^2 - 1,200 = 984

4x^2 + 140x - 984 = 0

x^2 + 35x - 246 = 0

Quadratic formula gives x = 6.

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It is true that (52 * 42) - 1,200 = 984, but you need to divide that 12 ft number by two since the walkway has, how shall I say, two North-South avenues and two East-West avenues.