   Chapter 8.2, Problem 25E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# In Exercises 25 and 26, give a paragraph form of proof.Provide drawings as needed. Given: Equilateral ∆ A B C with each side of length s Prove: A A B C =   S 2 4 3 (HINT: Use Heron’s Formula.)

To determine

To Prove:

Area of the equilateral triangle ABC with each side of length s is given by AABC= S243.

Explanation

Proof:

Let’s consider a ABC with each side of length 'S'.

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 all sides are of equal length 'S', the lengths lengths a, b and c becomes

a=b=c=S

Substituting the above values in the semiperimeter formula,

s=12a+b+c=12S+S+S=3S2

Applying the Heron’s formula for ABC,

AABC=

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