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The lengths of the sides of isosceles triangle ABC are 3x + 62, 7x + 30, and 5x + 60 feet. What is the least possible number of feet in the perimeter of ABC?

 Feb 17, 2022
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We have 3 equations that give us possible values for  x

!st....assume  that  these two sides are equal

3x + 62 = 7x + 30

   62 - 30  = 7x - 3x

       32  = 4x

         x =  8                        and the perimeter  =  3(8)+ 62 + 7(8)+ 30 + 5(8) + 60    = 272

 

Next assume that these two sides are equal

3x + 62  = 5x + 60

62 - 60  = 5x - 3x

2  = 2x

x = 1                               The perimeter  =  3(1) + 62  + 7(1)  + 30  + 5(1)  + 60 =   167

 

 

Finally, assume  that

7x + 30 = 5x + 60

7 - 5x  = 60 -30

2x = 30

x = 15....    it's obvious that this  value of x will lead to the greatest perimeter

 

So....the perimeter  is the least  when  3x + 62 = 5x + 60  and the perimeter  = 167

 

cool cool cool

 Feb 17, 2022

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