A rectangle with integer side lengths has perimeter 10. What is the gr

Question

A rectangle with integer side lengths has perimeter 10. What is the greatest number of these rectangles that can be cut from a piece of paper with width 24 and length 60?

A. 144
B. 180
C. 240
D. 360
E. 480

Archit3110 · Answer

2 * (l+b) = 10
l+b= 5
so as to get greatest no we have make either l or b least i.e 4+1
so
24*60 / 4* 1 = 360 
IMO D

Papist · Answer

Since the goal is to maximize the number of rectangles, we need to determine the smallest possible area of a rectangle with a perimeter of 10 (since diving the large piece of paper by that amount will yield the largest quotient).

The possible rectangles are 1,1,4,4 => A = 4 and 2,2,3,3 => A = 6

Divide the area of the paper (60*24 = 1440) by the smaller area of 4 and you get 360. The answer is D.

fireagablast · Answer

Maximize the number of rectangles by minimizing the size of the rectangles (area)

P=10
2L + 2W = 10 --> min area when difference in length and width is greatest
L=4 W=1

Area rectangle = 4*1

60*24/4 = 60*6 = 360 rectangles

GMATGuruNY · Answer

If x and y are positive integers such that their sum is a CONSTANT:
The GREATEST possible value of xy will be yielded when x and y are AS CLOSE TO EACH OTHER AS POSSIBLE.
The LEAST possible value of xy will be yielded when x and y are AS FAR FROM EACH OTHER AS POSSIBLE.
Given x+y=100, where x and y are positive integers:
Greatest option for xy = 50*50 = 2500
Least option for xy = 1*99 = 99
In short:
To MAXIMIZE the product, MINIMIZE the difference.
To MINIMIZE the product, MAXIMIZE the difference.

A rectangle with integer side lengths has perimeter 10: 
2L + 2W = 10
L+W = 5

What is the greatest number of these rectangles that can be cut from a piece of paper with width 24 and length 60? 
To maximize the number of rectangles, we must minimize the value of LW -- the area of each rectangle.
As noted above:
To minimize the product of L and W, we must maximize the difference between L and W, as follows:
L=4, W=1, area = 4*1 = 4
Thus:
Greatest number of rectangles  = \frac{paper-area}{rectangle-area} = \frac{24*60}{4} = 360

D

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A rectangle with integer side lengths has perimeter 10. What is the gr

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A rectangle with integer side lengths has perimeter 10. What is the gr

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