Answer:
The lenghts of the sides are: 8 inches, 32 inches, 36 inches.
Step-by-step 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: [tex]\frac{8x}{2} = 4x[/tex]
The third measure is of [tex]\frac{9x}{2}[/tex]
So the perimeter will be of:
[tex]x + 4x + \frac{9x}{2} = 76[/tex]
[tex]5x + \frac{9x}{2} = 76[/tex]
[tex]\frac{10x}{2} + \frac{9x}{2} = 76[/tex]
[tex]\frac{19x}{2} = 76[/tex]
[tex]19x = 76*2[/tex]
Simplifying by 19
[tex]x = 4*2 = 8[/tex].
So, dimensions of:
[tex]8, 4*8 = 32, \frac{9*8}{2} = 36[/tex]
The lenghts of the sides are: 8 inches, 32 inches, 36 inches.
