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    IBMediumAlgebra7–9

    Width of a Path Around a Pool

    Largura de um Passeio à Volta de uma Piscina

    A rectangular pool measures 88 m by 55 m. A path of uniform width runs all the way around it. The pool and path together cover 108 m2108 \text{ m}^{2}. Find the width of the path.

    Call the width xx and write the outer rectangle's two sides in terms of it. The path lies on both ends of each side, which is what decides how many times xx appears in each factor.

    Solution

    Step 1 of 8

    1. 1.The outer rectangle is (8+2x)(8 + 2x) by (5+2x)(5 + 2x):