Question

The ratio of the measures of the sides of a triangle is 2:8:9. If the perimeter of the triangleis 76 inches, find the length of each side. for geometry

Answer 1

The lenghts of the sides are: 8 inches, 32 inches, 36 inches.

Explanation:

Perimeter of a triangle:

The perimeter of a triangle is given by the sum of it's sides dimensions.

The ratio of the measures of the sides of a triangle is 2:8:9.

This means that their measures are:

The first measure is x

The second measure is of:
`(8x)/(2) = 4x`

The third measure is of
`(9x)/(2)`

So the perimeter will be of:

`x + 4x + (9x)/(2) = 76`

`5x + (9x)/(2) = 76`

`(10x)/(2) + (9x)/(2) = 76`

`(19x)/(2) = 76`

`19x = 76*2`

Simplifying by 19

`x = 4*2 = 8`.

So, dimensions of:

`8, 4*8 = 32, (9*8)/(2) = 36`

The lenghts of the sides are: 8 inches, 32 inches, 36 inches.