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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Section
BuyFindarrow_forward

Elementary Geometry For College St...

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

A circle is inscribed in an isosceles triangle with legs of length 10 in. and a base of length 12 in. Find the length of the radius of the inscribed circle.

To determine

To find:

The length of the radius of the inscribed circle.

Explanation

Formula used:

Radius of incircle:

radiusincircle=AreaofincircleperimeterofincircleAreaofincircle (A)=s(sa)(sb)(sc)perimeterofincircle (s)=a+b+c2

Given:

A circle is inscribed in an isosceles triangle with legs of length 10 in. and a base of length 12 in.

Calculation:

An isosceles triangle with legs of length 10 in. and a base of length 12 in.

We sketch the figure of the triangle of the inscribed circle.

Consider the measures of legs of an isosceles triangle 10 and 10. And measures of base of an isosceles triangle 12.

Next we find perimeter of triangle,

Let a=10,b=10,andc=12

s=10+10+122s=322s=16

Then we find area of triangle,

Areaofincircle A=16(1610)(16610)(1612)=16(6)(6)(4)

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