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12 Days of Christmas GMAT Competition with Lots of Fun
Is the perimeter of a rectangle more than 60 cm ?
(1) The area of the rectangle is 226 cm^2.
(2) The length of a diagonal of the rectangle is 30 cm.
M36-92
Is the perimeter of a rectangle more than 60 cm ?
(1) The area of the rectangle is 226 cm^2.
(2) The length of a diagonal of the rectangle is 30 cm.
M36-92
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12 Nov 2021, 07:43
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Official Solution:
Is the perimeter of a rectangle more than 60 cm ?
(1) The area of the rectangle is 226 cm^2.
Given \(ab = 226\).
Now, for rectangles with a fixed area, a square has the minimum perimeter. So, the minimum perimeter will occur when \(a=b\). In this case, we'd have \(a^2=226\).
\(a=15.something\) and thus the perimeter is \(4*15.something=60.something>60\). As even the minimum possible perimeter is more than 60 cm, then the actual perimeter, whatever it is, is also more than 60 cm. Sufficient.
(2) The length of a diagonal of the rectangle is 30 cm.
The diagonal, the length and the width of a rectangle form a triangle and in a triangle the length of any side must be smaller than the sum of the other two sides. So, \(a+b>30\) and thus \(perimeter=2(a + b) > 60\) Sufficient.
Answer: D
General Discussion
statement 1:
Area is 226 cm^2
assume Square, l=b
then l^2 = 226
l=15.xx (approx)
so perimeter 4l is more than 60. For rectangle then l is greater than breadth. so obviously perimeter is greater than 60
Hence Statement 1 is sufficient
Statement 2:
hypotenuse is 30. That means sum of two sides should be greater than 30. Hence perimeter will be greater than 60.
So Statement 2 is also sufficient.
Hence option D
Area is 226 cm^2
assume Square, l=b
then l^2 = 226
l=15.xx (approx)
so perimeter 4l is more than 60. For rectangle then l is greater than breadth. so obviously perimeter is greater than 60
Hence Statement 1 is sufficient
Statement 2:
hypotenuse is 30. That means sum of two sides should be greater than 30. Hence perimeter will be greater than 60.
So Statement 2 is also sufficient.
Hence option D
