Answer:
The lengths of the three sides are 30 cm, 41 cm, and 66 cm.
Explanation:
The perimeter of a triangle is the sum of the length of the three sides.
You are given expressions for the lengths of the sides, so you can add the expressions and find an expression for the perimeter of the triangle.
The sides measure x + 7, 2x - 5, and 3x - 3.
We add these three lengths to find the expression for the perimeter.
x + 7 + 2x - 5 + 3x - 3 = 6x - 1
The expression for the perimeter is 6x - 1.
We are told the perimeter is 137 cm, so 6x - 1 must equal 137.
6x - 1 = 137
Now we solve for x.
Add 1 to both sides.
6x = 138
Divide both sides by 6.
x = 23
Now that we know the value of x, we replace x in each expression representing a side length to find each actual side length.
x + 7 = 23 + 7 = 30
2x - 5 = 2(23) - 5 = 46 - 5 = 41
3x - 3 = 3(23) - 3 = 69 - 3 = 66
The lengths of the three sides are 30 cm, 41 cm, and 66 cm.