the perimeter of a triangle is 205. one side is 10 longer than the shortest side. the third side is 5 less than twice the shortest side.how long is each side

Let x = the shortest side

x + 10 + x + 2x-5 = 205

4x + 5 = 205
4x = 200
x = 50

To find the lengths of the sides of the triangle, we can solve the given information step by step. Let's denote the shortest side as "x".

1. According to the given information, one side is 10 longer than the shortest side, so we can express this side as "x + 10".

2. The third side is 5 less than twice the shortest side, which can be expressed as "2x - 5".

Now, we can write the equation for the perimeter of the triangle:
Perimeter = x + (x + 10) + (2x - 5)

Given that the perimeter is 205, we can solve the equation to find the value of "x":

205 = x + (x + 10) + (2x - 5)

Simplifying the equation:
205 = 4x + 5

Now, subtract 5 from both sides:
200 = 4x

Divide both sides by 4:
x = 50

So, the shortest side of the triangle is 50.

To find the lengths of the other two sides:
1st side: x + 10 = 50 + 10 = 60
2nd side: 2x - 5 = 2(50) - 5 = 100 - 5 = 95

Therefore, the lengths of the sides of the triangle are 50, 60, and 95.