Question

A rectangle with integer side length has perimeter $10$. What is the greatest numbers 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. $480$

Answer 1

The correct option is D $360$

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

$\left(i\right)2\times 3$ rectangle of area $6$

$\left(ii\right)1\times 4$ rectangle of area $4$

The piece of paper has area $24\times 60=1400$

This can be divided into $12\times 20=240$ rectangles with sides $2\times 3$

It can be divided into $24\times 15=360$ recatngles with sides $1\times 4$

So, the greatest number of rectangles is $360$