College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Section 1.5 - Applications and Modeling with Quadratic Equations - 1.5 Exercises - Page 119: 20

Answer

The dimensions of the rectangle are 100 m x 50 m. If the length is 100m, the width is 50m. If the length is 50m, the width is 100m.

Work Step by Step

The perimeter is 300 meters and is represented by 2x+2y. The area is 5000 square meters and is represented by xy. $$2x+2y=300$$ $$xy=5000$$ $$x=\frac{5000}{y}$$ $$2(\frac{5000}{y})+2y=300$$ $$\frac{10000}{y}+2y=300$$ $$10000+2y^2=300y$$ $$2y^2-300y+10000=0$$ $$y^2-150y+5000=0$$ $$(y-100)(y-50)=0$$ $$y=100,50$$ $$xy=5000$$ $$100x=5000$$ $$x=50$$ $$xy=5000$$ $$50x=5000$$ $$x=100$$ The dimensions of the rectangle are 100 m x 50 m. If the length is 100m, the width is 50m. If the length is 50m, the width is 100m.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.