Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 8 - Section 8.2 - Perimeter and Area of Polygons - Exercises - Page 361: 46a



Work Step by Step

(9,10,17) Using Heron's formula if three sides of a triangle have length a,b,c then area A of a triangle is A = $\sqrt s(s-a)(s-b)(s-c)$ where s = $\frac{a+b+c}{2}$ Lets take a=9 b=10 and c=17 s = $\frac{9+10+17}{2}$ = 18 A = $\sqrt 18(18-9)(18-10)(18-17)$ =$\sqrt 18 *9 * 8 *1$ =36 $unit^{2}$ If a,b,c be the integer length of the sides of the triangle. If area of the triangle is also an integer than (a,b,c) is known as heron triplet. So area is integer i.e. 36 so (9,10,17) is a heron triples.
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