Question

The lengths of the sides of a triangle are in the extended ratio 6 ​: 7 ​: 10. The perimeter of the triangle is 92 cm. What are the lengths of the​ sides?

Answer 1

Explanation:

`\underline{ \underline{ \text{Given}}} :`

• The ratios of length : 6 : 7 : 10
• Perimeter of a triangle = 92 cm

Let the lengths of a triangle be 6x , 7x and 10x.

`\underline{ \underline{ \text{To \: find}}} :`

• Lengths of the side

`\underline{ \boxed{ \text{Sum \: of \: all \: sides \: of \: triangle = Perimeter \: of \: a \: triangle}}}`

⟹
`\sf{6x + 7x + 10 = 92}`

Solve for x

⟹
`\sf{23x = 92}`

⟹
`\sf{ (23x)/(23) = (92)/(23)}`

⟹
`\sf{x = 4}` cm

Now , Replacing the value of x :

⟼
`\sf{6x = 6 *4 = 24}` cm

⟼
`\sf{7x = 7 * 4 = 28}` cm

⟼
`\sf{10x = 10 * 4 = 40}` cm

Hence , the sides of the triangle are 24 cm , 28 cm and 40 cm.

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