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Geometry

by Prajakt » Fri Sep 07, 2012 8:58 pm
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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by Anurag@Gurome » Fri Sep 07, 2012 9:13 pm
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
Perimeter of rectangle = 2(L + W)
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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by neelgandham » Sat Sep 08, 2012 12:33 am
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!
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