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: ![\frac{8x}{2} = 4x](https://tex.z-dn.net/?f=%5Cfrac%7B8x%7D%7B2%7D%20%3D%204x)
The third measure is of ![\frac{9x}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B9x%7D%7B2%7D)
So the perimeter will be of:
![x + 4x + \frac{9x}{2} = 76](https://tex.z-dn.net/?f=x%20%2B%204x%20%2B%20%5Cfrac%7B9x%7D%7B2%7D%20%3D%2076)
![5x + \frac{9x}{2} = 76](https://tex.z-dn.net/?f=5x%20%2B%20%5Cfrac%7B9x%7D%7B2%7D%20%3D%2076)
![\frac{10x}{2} + \frac{9x}{2} = 76](https://tex.z-dn.net/?f=%5Cfrac%7B10x%7D%7B2%7D%20%2B%20%5Cfrac%7B9x%7D%7B2%7D%20%3D%2076)
![\frac{19x}{2} = 76](https://tex.z-dn.net/?f=%5Cfrac%7B19x%7D%7B2%7D%20%3D%2076)
![19x = 76*2](https://tex.z-dn.net/?f=19x%20%3D%2076%2A2)
Simplifying by 19
.
So, dimensions of:
![8, 4*8 = 32, \frac{9*8}{2} = 36](https://tex.z-dn.net/?f=8%2C%204%2A8%20%3D%2032%2C%20%5Cfrac%7B9%2A8%7D%7B2%7D%20%3D%2036)
The lenghts of the sides are: 8 inches, 32 inches, 36 inches.