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The perimeter of an isosceles triangle is 36 centimeters and two sides of the triangle are in the ratio 2:7. What is the number of centimeters in the length of the longest side?

 Oct 14, 2020
 #1
avatar+27725 
+1

From a Google search
According to the first triangle inequality theorem, the lengths of any two sides of a triangle must add up to more than the length of the third side. This means that you cannot draw a triangle that has side lengths 2, 7 and 12, for instance, since 2 + 7 is less than 12.

Possible combos:

 

 

 2x + 7x    < 36-9x

18x < 36

x < 2                    

x =1      2   7  27     

x=2      4 14  18                   These do not meet the triangle inequality theorem above        

x = 1.5         5   17.5   13.5  <====  possible          5:17.5   =  2:7             longest = 17.5 cm

 
 Oct 15, 2020
 #2
avatar+1374 
+2

The perimeter of an isosceles triangle is 36 centimeters and two sides of the triangle are in the ratio 2:7. What is the number of centimeters in the length of the longest side?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

An isosceles triangle is a triangle with two equal sides.

 

If the ratio of the two sides is 2:7 then the ratio of all 3 sides is 2:7:7  

 

 The length of the longest side is:>         7(36 / 16) = 15.75 cm 

 
 Oct 15, 2020
edited by Dragan  Oct 15, 2020
 #3
avatar+27725 
+1

Agree!   Sorry....didn't see 'isosceles' in the Q !     ~ EP

 
ElectricPavlov  Oct 15, 2020

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