Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 10 - Geometry - 10.4 Area and Circumference - Exercise Set 10.4: 11

Answer

30 $in^{2}$

Work Step by Step

Area of triangle = $\frac{1}{2} \times b \times h$ b= 12 in h is unknown Since the triangle is a right-angled triangle, h can be found using the Pythagorean Theorem which states that that the square of the hypotenuse is equal to the sum of the square of the other two sides $12^{2}+h^{2}=13^{2}$ Solving algebraically: $h^{2}=13^{2}-12^{2}$ $h^{2}=25$ $h=\sqrt 25 =5$ Thus, Area of triangle = $\frac{1}{2} \times b \times h$ = $\frac{1}{2} \times 12 \times 5$ = 30 $in^{2}$
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