Bunuel wrote:
Martin planted a rectangular garden with dimensions 20 feet by 30 feet and then surrounded the garden with a rectangular brick walkway of uniform width (represented by the shaded area in the drawing above). If the area of the walkway equals the area of the garden, what is the width of the walkway?
(A) 1 foot
(B) 3 feet
(C) 5 feet
(D) 8 feet
(E) 10 feet
Attachment:
2017-07-11_1344.png
Here's an algebraic solution...
There are two areas to consider:
1) area of rectangular garden
2) area of walkway
We know the area of the garden = (20)(30) = 600 square feet.
Since the area of the walkway EQUALS the area of the garden, the area of the walkway also equals 600 square feet.
So, the area of the OUTER rectangle (which includes both the garden and the walkway) = 600 + 600 =
1200What are the dimensions of the OUTER rectangle?
They are
20 + 2x by 30 + 2xWe can write:
(20 + 2x)(30 + 2x) =
1200Expand and simplify: 600 + 100x + 4x² = 1200
Rearrange to get: 4x² + 100x - 600 = 0
Divide both sides by 4 to get: x² + 25x - 150 = 0
Factor: (x + 30)(x - 5) = 0
So, EITHER x = -30 OR x = 5
Since the width of the walkway (x) cannot be negative, we can conclude that x = 5
Answer:
Cheers,
Brent
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