   Chapter 8.2, Problem 26E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 25 and 26, give a paragraph form of proof.Provide drawings as needed. Given: Isosceles ∆ M N Q with Q M = Q N = s and M N   =   2 a Prove: A M N Q = a s 2 - a 2 (NOTE: s > a . )

To determine

To Prove:

Area of the isosceles triangle MNO with each side of lengths QM=QN=s and MN = 2a is given by AMNQ=as2-a2.

Explanation

Proof:

Let’s consider a MNO with each side of lengths QM=QN=s and MN = 2a.

If the three sides of a triangle have lengths a, b and c then the area A of the triangle is given by A=s(s-a)(s-b)(s-c),

where the semiperimeter of the triangle is s=12(a+b+c).

As two of the sides are of equal length 's' and the other side is of length 2a, the lengths a, b and c becomes

a=s;b=s; and c=2a

Substituting the above values in the semiperimeter formula,

s=12a+b+c=12s+s+2s=s+a

Applying the Heron’s formula for MNO,

AM

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