Question

The longest side of a triangle is 3 times the shortest side and the third side

is 2 cm shorter than the longest side. If the perimeter of the triangle is

atleast 61 cm find the minimum length of the shortest side.

Answer 1

Answer :-

Let the length of shortest side of this given triangle be equal to x cm.

Therefore,

Longest side of this triangle = thrice the shortest side = 3 × x = 3x

The third side = 3x - 2

Given,

Perimeter of this triangle = 61 cm

Substituting the values of the sides that we have assumed

x + 3x + ( 3x - 2 ) = 61 cm

This is a linear equation in 1 variable i.e x

Solving this linear equation using transposition : -

x + 3x + 3x - 2 = 61

7x - 2 = 61

7x = 63

x = 63/7

x = 9


So,

the length of the shortest side of this given triangle = x = 9 cm.

Answer 2

Let us consider the problem:

longest of the shortest side be x cm

therefore, length =3 shorter side =3x

and length of third side =(3x−2)cm

now,

perimeter = sum of there side = x+3x+(3x−2)

= x + 3x+ 3x−2

= 7x−2

Given to:

perimeter of triangle is at least =61cm

there fore, ≥61

7x−2≥61

7x≥61+2

7x≥63

x≥63/7

x≥9

hence the minimum leghth of the shortest side is 9cm