Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.7 - Modeling with Equations - 1.7 Exercises - Page 76: 43

Answer

60ft by 40ft

Work Step by Step

Perimeter = 200ft = 2x+2y Area = 2400 ft$^{2}$ = (x)$\times$(y) Express y from the second equation: y=$\frac{2400}{x}$ Plug it into the first equation 200=2x+2$\times$$\frac{2400}{x}$ 200=2x+$\frac{4800}{x}$ 200x=2$x^{2}$ +4800 0=2$x^{2}$ -200x +4800 Quadratic formula: $200^{2}$-4$\times$2$\times$4800=1600 x=$\frac{200 + or -\sqrt 1600}{4}$ Dimensions can't be negative, so the only answer is: x=60 Plug this number into the first equation: 200=2$\times$60+2y 80=2y y=40
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