Question

construct a triangle abc in which three sides are in the ratio of 1:3:5 and its perimeter is 13.5

Answer 1

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Given side are in the ratio 1:3:5

Let the sides of triangle are x, 3x, 5x

Now perimeter of triangle = 13.5

=> x+3x+5x = 13.5

=> 9x = 13.5

=> x = 13.5/9

=> x = 1.5

So side of triangle are = 1.5, 1.5*3, 1.5*5

                                 = 1.5 cm, 4.5 cm, 7.5 cm

 

Now in a triangle, sum of two sides should be greater than the third side

=> 1.5+4.5 = 6.0

Now 6.0 < 7.5  

So triangle is not possible for given ratio.

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