The answer is 64. It's pretty algebra intensive so I might cut through a few steps.
First width = length of square = x + 5
First let's find x in the walkway;
Area of bottom most side is ((x+5)+x+x)x
Area of top most side is the same so total area of bottom and top sides =
2(3x+5)x.
Area of two sides of walkway = (x+5)x + x(x+5)
Total area = 2(3x+5)x + 2x(x+5) = 132
in short
2x^2 + 5x - 33 = 0
So x = 3 or x = -5.5. x can only be positive. So we know width = length of square = 3 + 5 = 8. So area = 8^2 = 64
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Source: Beat The GMAT — Data Sufficiency |
IMO -B
Length of each side of patio = (x+5)
Length of each side of the outer square = 3x + 5
Given (3x+5)^2 - (x+5)^2 = 132
(9x^2 + 25+ 30x ) - (x^2 + 10x + 25) = 132
8x^2 + 20x - 132 =0
2x^2 + 5x - 33 = 0
2x^2 -6x +11x - 33 = 0
2x(x-3) + 11(x-3)= 0
Hence x=3
Side of patio = x+5 = 8
Area = 8*8 = 64
Length of each side of patio = (x+5)
Length of each side of the outer square = 3x + 5
Given (3x+5)^2 - (x+5)^2 = 132
(9x^2 + 25+ 30x ) - (x^2 + 10x + 25) = 132
8x^2 + 20x - 132 =0
2x^2 + 5x - 33 = 0
2x^2 -6x +11x - 33 = 0
2x(x-3) + 11(x-3)= 0
Hence x=3
Side of patio = x+5 = 8
Area = 8*8 = 64
How you both are arriving at the above equation?Length of each side of patio = (x+5)
Length of each side of the outer square = 3x + 5
IMO : Length of each side of patio = 5
Length of each side of the outer square = 2x + 5
Let me know where I am wrong.
Hi Karangmat740 wrote:How you both are arriving at the above equation?Length of each side of patio = (x+5)
Length of each side of the outer square = 3x + 5
IMO : Length of each side of patio = 5
Length of each side of the outer square = 2x + 5
Let me know where I am wrong.
It is mentioned that " side of patio is 5 metres greater than the width of the walkway(x) "
Hence we get side of patio = x+5
