A triangle has sides according to the extended ratio: 5:9:11. If the perimeter of the triangle is 100, write and solve an equation on x that models this situation. Use that value of x to find the lengths of the sides.
Let the sides of the triangle be 5x, 9x, and 11x.
The perimeter of the triangle is the sum of all the sides, so we have:
5x + 9x + 11x = 100
25x = 100
x = 4
Therefore, the lengths of the sides are:
5x = 5(4) = 20
9x = 9(4) = 36
11x = 11(4) = 44
So, the lengths of the sides are 20, 36, and 44.