A rectangular poster has an area of 360 square inches. A copy of the poster is made in which the

Question

A rectangular poster has an area of 360 square inches. A copy of the poster is made in which the length and width of the original poster are each increased by 20 % . What is the area of the copy, in square inches?

Accepted Answer

The correct answer is 518.4 . It's given that the area of the original poster is 360 square inches. Let l represent the length, in inches, of the original poster, and let w represent the width, in inches, of the original poster. Since the area of a rectangle is equal to its length times its width, it follows that 360 = l w . It's also given that a copy of the poster is made in which the length and width of the original poster are each increased by 20 % . It follows that the length of the copy is the length of the original poster plus 20 % of the length of the original poster, which is equivalent to l + 20 100 l inches. This length can be rewritten as l + 0.2 l inches, or 1.2 l inches. Similarly, the width of the copy is the width of the original poster plus 20 % of the width of the original poster, which is equivalent to w + 20 100 w inches. This width can be rewritten as w + 0.2 w inches, or 1.2 w inches. Since the area of a rectangle is equal to its length times its width, it follows that the area, in square inches, of the copy is equal to 1.2 l 1.2 w , which can be rewritten as 1.2 1.2 l w . Since 360 = l w , the area, in square inches, of the copy can be found by substituting 360 for l w in the expression 1.2 1.2 l w , which yields 1.2 1.2 360 , or 518.4 . Therefore, the area of the copy, in square inches, is 518.4 .

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