Elementary Geometry for College Students (7th Edition)

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 8 - Section 8.2 - Perimeter and Area of Polygons - Exercises - Page 370: 22

Answer

8 units

Work Step by Step

Lets assume that the side of square = x As we know the area of square = side * side = $x^{2}$ Perimeter of square = 4* side = 4x by given condition $x^{2}$ - 4x=32 $x^{2}$ - 4x - 32 = 0 $x^{2}$ - 8x +4x -32 = 0 x(x-8) +4(x-8)=0 (x+4) (x-8) = 0 x+4 = 0 x = -4 x-8 = 0 x =8 The length of the square cannot be negative so length of the square is 8 units.
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