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

2 Answers
Aug 22, 2016

Answer:

#360#

Explanation:

If a rectangle has perimeter #10# then the sum of its length and width is #5#, giving two choices with integer sides:

  • #2xx3# rectangle of area #6#
  • #1xx4# rectangle of area #4#

The piece of paper has area #24xx60 = 1440#

This can be divided into #12xx20=240# rectangles with sides #2xx3#.

It can be divided into #24xx15 = 360# rectangles with sides #1xx4#

So the greatest number of rectangles is #360#.

Aug 23, 2016

Answer:

#360#

Explanation:

Calling #S = 60 xx 24 = 2^5 xx 3^2 xx 5 xx 1# the problem can be stated as

Determine

#max n in NN^+#

such that

#n le S/(a cdot b)#
#a + b = 5#
#{a, b} in {1,2,3,4}#

giving the feasible pairs

#{1,4},{2,3}# and the desired result is

#n = 1440/4 =360#