Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Section 11.1 - Solving Quadratic Equations by Completing the Square - Exercise Set - Page 766: 78

Answer

Each side is 21.21 inches

Work Step by Step

We know that each side of a square is equal and two sides of a square along with a diagonal form a right angled triangle. In the figure, we consider the triangle as ACD where $AD=CD=x$ We will use Pythagoras theorem to find out the length of the equal sides of the triangle. By Pythagoras theorem, $P^2+B^2=H^2$ Where, P= Perpendicular B= Base H= Hypotenuse Here $P=B=x$ and $H=30$ Step-1 Substituting the formula: $x^2+x^2=30^2$ $2x^2=900$ Step-2 Divide both sides by 2 $x^2=\frac{900}{2}$ $x^2=450$ Step-3 Using the square root property $x=±\sqrt 450$ $x=±21.21 Since the side of a traingle cannot be negative, the length is approximately 21.21 inches. Therefore, each side of the square is 21.21 inches.
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