Question

The measure of the sides of an acute angled triangle is in the ratio 2 : 5 : 7 the perimeter of the triangle is 21 cm

Find the length of each side .

Answer 1

3 cm, 7.5 cm and 10.5 cm.

Step-by-step explanation:

Let's say that the three sides of the acute angled triangle are 2x, 5x and 7x.

As we know that perimeter of acute angled triangle is equal to the sum of all sides of the triangle.

`\sf 2x + 5x + 7x = 21`

`\sf 7x + 7x = 21`

`\sf 14x = 21`

Divide both sides by 14,

`\bf x = 1.5`

The three sides of the acute angled triangle are 2x, 5x and 7x. To find the length of each side, we can simply substitute the value of x in the sides of triangle.

First side =
`\sf 2x`

`\bf 2(1.5) = 3 cm`

Second side =
`\sf 5x`

`\bf 5(1.5) = 7.5 cm`

Third side =
`\sf 7x`

`\bf 7(1.5) = 10.5 cm`

Therefore, the measure of the sides of an acute angled triangle are 3 cm, 7.5 cm and 10.5 cm.