Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Appendix A - A.4 - Quadratic Equations - Exercises - Page 561: 33

Answer

Width: $5$ units Length: $8$ units The dimension of the rectangle is $5$ x $8$ units.

Work Step by Step

Let $x = $ the width of the rectangle $x(x+3) = 40$ $x^{2} + 3x = 40$ $x^{2} + 3x - 40 = 0$ Find two numbers that can be multiplied together to get $-40$ and can be added together to get $3$. $= -5$ and $8$ $x^{2} - 5x + 8x - 40 = 0$ $x(x - 5) + 8(x-5) = 0$ $(x+8)(x-5) = 0$ $x = -8, 5$ Given that $x \ne -8$, then $x = 5$ units. Width: $5$ units Length: $x + 3$ $= 5 + 3$ $= 8$ units
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