The printed matter on a 14 by 20 centimeter page of a book must cover 160 square centimeters. If all margins are to be the same width, how wide should they be?
A) $2 \mathrm{~cm}$
B) $1 \mathrm{~cm}$
C) $3 \mathrm{~cm}$
D) $4 \mathrm{~cm}$

Question

Quizplus · Accepted Answer

The total area of the page is $14 \times 20 = 280$ square centimeters. The area to be covered by printed matter is 160 square centimeters, leaving $280 - 160 = 120$ square centimeters for the margins. Since the margins are uniform and surround the printed area, we divide this area by the perimeter of the printed area to find the width of a margin. However, we don't need to calculate the perimeter directly; we can set up an equation based on the dimensions of the printed area and the margins. Let $w$ be the width of the margins. The dimensions of the printed area would then be $(14 - 2w) \times (20 - 2w)$. The equation for the area of the printed matter is $(14 - 2w)(20 - 2w) = 160$. Simplifying, we find $w = 2$ cm.

The Printed Matter on a 14 by 20 Centimeter Page 2 cm2 \mathrm{~cm}2 cm

The Printed Matter on a 14 by 20 Centimeter Page $2 \mathrm{~cm}$