Cutting a sheet of paper

Algebra Level 2

A 2 m 2 \text{ m} by 2 m 2 \text{ m} sheet of paper is to be cut into 2 cm 2 \text{ cm} by 10 cm 10 \text{ cm} rectangles. What is the maximum number of such rectangles that can be cut from the sheet of paper?

3000 2000 500 1500 1000

Hana Wehbi by Hana Wehbi , 51, USA

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2 solutions

Tom Engelsman
Aug 16, 2017

The area of one rectangle is just 0.02 × 0.1 = . 002 0.02 \times 0.1 = .002 square meters. Hence, the maximum number of cut rectangles is:

( 2 × 1 0 − 3 ) ⋅ N = 4 ⇒ N = 2000 . (2 \times 10^{-3}) \cdot N = 4 \Rightarrow N = \boxed{2000}.

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Nice Solution :)

Hana Wehbi - 3 years, 9 months ago

You're assuming that all of the paper can be used. Does the answer change if we want a 0.0002 × 10 0.0002 \times 10 rectangle which has the same area?

Calvin Lin Staff - 3 years, 9 months ago
Hana Wehbi
Aug 16, 2017

Let M M be the maximum number of rectangles, then M = 200 10 × 200 2 = 2000 M= \frac{200}{10}\times \frac{200}{2} = 2000 .

1m= 100cm

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