Attached is a question from GMAT Prep Test 2.
Please advise how to achieve the result.
Answer: B
Thanks,
K
GMAT Test 2_PS Square #15
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Area of square garden = A sq ftkwah wrote:Attached is a question from GMAT Prep Test 2.
Please advise how to achieve the result.
Answer: B
Thanks,
K
Perimeter of square garden = P ft
A = 2P + 9
Let us assume that each side of the square garden = sÂ² sq ft
Then A = sÂ² and P = 4s
So, A = 2P + 9 implies sÂ² = 2 *(4s) + 9
sÂ² = 8s + 9
sÂ²  8s  9 = 0
sÂ²  9s + s  9 = 0
s(s  9) + 1(s  9) = 0
(s + 1)(s  9) = 0
s = 9, (s = 1 is not possible, as side cannot be negative)
Therefore, perimeter of square garden = 4 * 9 = 36 ft
The correct answer is B.
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Let us assume the side of the square to be 'a' cm.
So, its area A = a^2 sq.cm
Perimeter P = 4a.
Given A = 2P + 9
We will now plug in the values of A and P in the above equation.
We get,
a^2 = 2(4a) + 9
a^2 = 8a + 9
==> a^2  8a  9 = 0
==> a^2  9a + a  9 = 0 [factors 0f 9 such that difference is 8 and product is 9 is 9 and 1]
==> a(a  9) + 1(a  9) = 0
==> (a  9)(a + 1) = 0
==> a = 9 or 1.
We will consider 'a' = 9 as the measurement of length cannot be < 0.
Hence, the perimeter P = 4a = 4(9) = 36cm.
So, its area A = a^2 sq.cm
Perimeter P = 4a.
Given A = 2P + 9
We will now plug in the values of A and P in the above equation.
We get,
a^2 = 2(4a) + 9
a^2 = 8a + 9
==> a^2  8a  9 = 0
==> a^2  9a + a  9 = 0 [factors 0f 9 such that difference is 8 and product is 9 is 9 and 1]
==> a(a  9) + 1(a  9) = 0
==> (a  9)(a + 1) = 0
==> a = 9 or 1.
We will consider 'a' = 9 as the measurement of length cannot be < 0.
Hence, the perimeter P = 4a = 4(9) = 36cm.