Question

The sides of a triangle are in the ratio 1/2:1/3:1/4 and its perimeter is 108 cm. The lenght of the longest side

Answer 1

$\underline{\underline{\bold{Question:}}}$

The sides of a triangle are in the ratio 1/2:1/3:1/4 and its perimeter is 108 cm. The length of the longest side :

$\tt{Solution:}$

The ratio of the sides of a triangle :

$\tt{=\dfrac{1}{2}:\dfrac{1}{3}:\dfrac{1}{4}}\\\\\\\tt{=\dfrac{1}{2}*12:\dfrac{1}{3}*12:\dfrac{1}{4}*12}\\\\\\\tt{=6:4:3.}$

Let the sides of the triangle be 6x m , 4x m and  3x m .

$\boxed{\bold{Perimeter=Sum\:of\:all\:3\:sides.}}$

According to question ,

The perimeter of the triangle = 108 m.

$\implies\bold{6x+4x+3x=108}\\\\\\\implies\bold{13x=108}\\\\\\\implies\bold{x=\dfrac{108}{13}.}\\\\\\\boxed{\boxed{\bold{Longest\:side=6x=6*\dfrac{108}{13}=\dfrac{648}{13}=49\dfrac{11}{13}m.}}}$

Answer 2

$ratio = \frac{1}{2} : \frac{1}{3} : \frac{1}{4}$

Let 1st Side=x/2

Let 2nd Side=x/3

Let 3rd Side=x/4

Sum of all side is its Perimeter.

Perimeter=108 cm

$\frac{x}{2} + \frac{x}{3} + \frac{x}{4} = 108 \\ \\ \frac{6x + 4x + 3x}{12} = 108\: \: \: (lcm = 12) \\ \\ \frac{13x}{12} = 108 \\ \\ x = 108 \times \frac{12}{13} \\ \\ x = 8.30 \times 12 \\ \\ x = 99.6$

1st Side=X/2

=99.6/2

=49.8 cm

2nd Side=X/3

=99.6/3

=33.2 cm

3rd Side=X/4

=99.6/4

=24.9 cm

$\boxed{\mathbf{Longest\:Side=49.8\:cm}}$