If the perimeter of a certain rectangle is 76 and its areais 360 then what is the length of its shortest side?
A. 12
B. 18
C. 20
D. 36
E. 40
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Anurag@Gurome
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Perimeter of rectangle = 2(L + W)Prajakt wrote:If the perimeter of a certain rectangle is 76 and its areais 360 then what is the length of its shortest side?
A. 12
B. 18
C. 20
D. 36
E. 40
Area = L * W
Now, 2(L + W) = 76
L + W = 38 ... Equation (1)
LW = 360 ... Equation (2)
From Equations (1) and (2), L(38 - L) = 360
L² - 38L + 360 = 0
(L - 18)(L - 20) = 0
L = 18, 20 implies W = 20, 18
Therefore, length of the shortest side = 18 units
The correct answer is B.
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neelgandham
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If the perimeter of a certain rectangle is 76 and its area is 360 then what is the length of its shortest side?
Since Anurag has already solved the problem using variables, I will try and solve it in a slightly logical way.
Perimeter of a rectangle = 2*(Length of the rectangle + Breadth of the rectangle) = 76
Length of the rectangle + Breadth of the rectangle = 38.
The values of Length and Breadth of the rectangle are equal if the rectangle is a square. Because the question already mentioned that there is a shorter side, the rectangle cannot be a square.
i.e. Length of the rectangle > Breath of the rectangle.
Length of the rectangle + Breadth of the rectangle = 38
Breadth of the rectangle + Breath of the rectangle< 38
Breadth of the rectangle < 38/2
Breadth of the rectangle < 19.
A. 12
B. 18
C. 20 - Eliminated.
D. 36 - Eliminated.
E. 40 - Eliminated.
Let us know check if the length of the shorter side is 12. If the breadth of the rectangle is 12, then the length of the rectangle is 38-12 = 26.
Area of the rectangle = 26*12 = Some value ending in 2. But the original area of the rectangle is 360(ends in 0). So, answer choice A is incorrect.
B it is!
Since Anurag has already solved the problem using variables, I will try and solve it in a slightly logical way.
Perimeter of a rectangle = 2*(Length of the rectangle + Breadth of the rectangle) = 76
Length of the rectangle + Breadth of the rectangle = 38.
The values of Length and Breadth of the rectangle are equal if the rectangle is a square. Because the question already mentioned that there is a shorter side, the rectangle cannot be a square.
i.e. Length of the rectangle > Breath of the rectangle.
Length of the rectangle + Breadth of the rectangle = 38
Breadth of the rectangle + Breath of the rectangle< 38
Breadth of the rectangle < 38/2
Breadth of the rectangle < 19.
A. 12
B. 18
C. 20 - Eliminated.
D. 36 - Eliminated.
E. 40 - Eliminated.
Let us know check if the length of the shorter side is 12. If the breadth of the rectangle is 12, then the length of the rectangle is 38-12 = 26.
Area of the rectangle = 26*12 = Some value ending in 2. But the original area of the rectangle is 360(ends in 0). So, answer choice A is incorrect.
B it is!
Anil Gandham
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Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
