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Two sides of an isosceles triangle are 10 inches and 20 inches.  What is the area of the triangle?

 Nov 12, 2020
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The two equal sides must  = 20.......here's why.....by the triangle inequality,  the sum of any two sides of a triangle must be greater than the remaining side....if the two equal sides   =10, then 10 + 10  =  20  which is NOT greater then the remaining side (20)

 

So....the sides must  be 20, 20  and 10

 

We can use something known as Heron's Formula to  solve this

 

First......sum the sides and divide by two  =  (20 + 20 + 10)  / 2  =  25

 

This is known as the semi-perimeter, S

 

The area  =   sqrt  [  S * (S -A) * (S -B) * (S-C)  ]    where A, B ,C  are the sides of the triangle

 

So we have

 

Area   =sqrt [  (25 * (25  -20) (25 -20) (25 -10) ] = sqrt  [ (25) * (5) (5) (15)] 

 

Area  =  sqrt  [ 25 * 5 * 5 * 15 ] =

 

Area  =sqrt [ 9375 ]  ≈  96.8  sq inches

 

 

cool cool cool

 Nov 12, 2020

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