Question

The sides of a triangle are in the ratio (1/2):(1/3):(1/4) and its perimeter is 104 cm.The length ofvthe longest side of the

Answer 1

$\mathfrak{Answer:}$

= 48 cm.

$\mathfrak{Step-by-Step\:Explanation:}$

$\underline{\underline{\bold{Given\;in\;the\;Question:}}}$

• Perimeter = 104 cm.

Ratio of sides of the triangle :

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

Let the common multiple be x.

So sides of triangle = 6x cm , 4x cm and 3x cm.

$\boxed{\bold{Perimeter=Sum\;of\;all\;sides}}\\\\\\\mathfrak{According\;to\;Question:}\\\\\\\implies\tt{6x+4x+3x=104}\\\\\\\implies\tt{13x=104}\\\\\\\implies\tt{x=\dfrac{104}{13}}\\\\\\\implies\tt{x=8.}\\\\\\\\\boxed{\boxed{\bold{Length\;of\;longest\;side=6x\;cm=6\times 8=48\;cm.}}}$

Answer 2

Sides are in ratio 1/2: 1/3: 1/4

Multiply by 12

12/2 : 12/3 : 12/4

6: 4: 3

And perimeter is 104

Let sides be 6x ,4x ,3x

6 x + 4 x +3x = 104

13x = 104

x= 8

So length of longest side = 6x = 6× 8 = 48 cm

✌✌Dr.Dhruv✌✌✌✌