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

Question

A rectangular garden is surrounded by a 3 ft. wide concrete sidewalk. If the length of the garden is 4 ft more than its width, and if the area of the sidewalk is 60 sq ft more than the area of the garden, then what is the length of the garden?

A. 6
B. 8
C. 10
D. 12
E. 14

Kudos for a correct solution.

A. 6 
B. 8 
C. 10 
D. 12 
E. 14

Kudos for a correct  solution .

bhatiamanu05 · Answer

Consider the rectangle length in L. According to question Breadth B = L-4
So Area of garden is = L*L-4 => L^2 - 4L
This garden is surrounded by 3 fit concrete walk. As per attached Fig.
a,b,c,d are equal and sum = 4*3*3 = 36
and rest of the area will be = 2(3*L + 3*(L-4)) =>12L-24
So total area of sidewalk = 36+12L-24 => 12L +12

So if equate area as per question : 12L+12 = L^2 - 4L + 60
=>L^2 - 16L +48 = 0
L = 4,12
L can't be 4 as B will be zero in that case.
So ans should be 12.

PareshGmat · Answer

Answer = D = 12 Refer diagram below: gar.png Let the width = x, then length = x+4 Area of garden (Green) = x(x+4) Area of side walk (Pink + White) = 3(x+6)*2 + 3(x+4)*2 = 6(2x+10) = 12(x+5) Given that x(x+4) + 60 = 12(x+5) x^2 + 4x = 12x x = 8 x+4 = 12

Bunuel · Answer

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: wp_img3.png 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).

OptimusPrepJanielle · Answer

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(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

HiLine · Answer

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

laxpro2001 · Answer

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?

rocky620 · Answer

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

GMATGuruNY · Answer

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!

D

bumpbot · Answer

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

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