A rectangular garden is surrounded by a 3 ft. wide concrete sidewalk.

MAGOOSH OFFICIAL SOLUTION:

This is a challenging geometry problem. Let the width of the garden be x, so the length is (x + 4). The garden itself would have an area of x(x + 4). Now, for the area of the sidewalk, consider this diagram:
Notice, the sidewalk can be subdivided into convenient pieces. There are two of the long horizontal rectangles at the top and bottom; each is 3(x + 4). There are two vertical side rectangles: each is 3x. Finally, there are four corner squares, each 3 x 3 = 9. The total area of the sidewalk is:

area of sidewalk = 6(x + 4) + 6x + 4*9 = 12x + 24 + 36 = 12x + 60

Now, we are told that
(area of sidewalk) = (area of garden) + 60
12x + 60 = x(x + 4) + 60
12x = x^2 + 4x
0 = x^2 - 8x = x(x - 8)

The solution x = 0 doesn’t make sense in the problem, so the only solution this gives is x = 8. This means, the garden is 8 x 12, and the length of the garden is 12.

Answer = (D).

Assume the width = x
Hence length = x + 4

Area of side walk plus garden= (x + 6)* (x + 4 + 6) {The sidewalk is present at both ends of the length and the breadth, hence we need to add 2*3}
Area of sidewalk = (x+6)(x+10) - x(x+4)

Given: Area of sidewalk - area of garden = 60, Hence
[(x+6)(x+10) - x(x+4)] - x(x + 4)= 60
x^2 + 16x + 60 - 2x^2 - 8x = 60
x^2 - 8x = 0
x(x - 8) = 0

Hence x = 8
Length = x + 4 = 12

Correct Option: D

Let the width of the garden be x.
Length of garden: x + 4
Width of garden: x + 6
Length of garden: x + 10

Total area of sidewalk and garden is twice area of sidewalk plus 60

(x+6)(x+10) = 2x(x+4) + 60

This leads to x^2 - 8x = 0, so x = 8

Therefore length of garden is 8 + 4 = 12

Bunuel
I'm guessing if it said "area enclosed by the side walk" we could have just taken the total area of the sidewalk minus the garden, right?

A quick method can be to use the equation:

Total area = Area of Sidewalk + Area of Garden
= (Area of garden + 60) + Area Of Garden
=2(Area Of garden) + 60

We can PLUG IN THE ANSWERS, which represent the length of the garden.
The correct answer is probably relatively large, given that the following difference must be yielded:
Sidewalk - garden = 60 square feet
Note:
The 3-foot wide sidewalk adds 6 feet to the length (3 feet to the left of the garden and 3 feet to the right) and 6 feet to the width (3 feet up and 3 feet down).

D: length of the garden = 12, implying that the width of the garden = 12-4 = 8
Area of the garden alone = 12*8 = 96
Area of the outer rectangle when the sidewalk is included = (12+6)(8+6) = 18*14 = 252
Area of the sidewalk = (outer rectangle) - (garden) = 252-96 = 156
Sidewalk - garden = 156-96 = 60 square feet
Success!

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