Explanation Given data: The area of the garden is 180 square yards. The dimensions of garden plus walk are 16 by 24 yards and the width of walk around the garden is x. Method/Formula used: The area A of a rectangular field of length l and width wis given by A = l × w . Calculation: Suppose l and w are the length and width of the garden respectively, and width of walk around thegarden is x. Then length of field garden plus walk is L = l + x + x = l + 2 x and the width of the field garden walk is W = w + x + x = w + 2 x . Thus, the dimensions of the garden plus walk are W = w + 2 x by L = l + 2 x yards. But the dimensions of garden plus walk are 16 by 24 yards. That implies W = 16 ⇒ w + 2 x = 16 ⇒ w = 16 − 2 x and L =24 ⇒ l + 2 x = 24 ⇒ l = 24 − 2 x . Thus the dimensions of the garden are 16 − 2 x by 24 − 2 x yards, so the area of the garden A = ( 24 − 2 x ) × ( 16 − 2 x ) square yards. But the area of the garden is 180 square yards, hence ( 24 − 2 x ) × ( 16 − 2 x ) = 180 (Factor out 2 from each bracket) 2 × ( 12 − x ) × 2 × ( 8 − x ) = 180 ⇒ 4 × ( 12 − x )

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ISBN: 9780134650111

Author: Martin-Gay

Publisher: PEARSON

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Chapter 13.7, Problem 62ES

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The width of walk around a garden.

Solution Summary: The author calculates the width of walk around a garden, based on the dimensions of the garden plus walk, which are 16 by 24 yards.

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