One side of an isosceles triangle is 15 cm shorter than the other 2 sides. The perimeter is 120 cm. How long are the sides of the triangle?
S = length of the short side in cm. Since the triangle has three sides:
S + (S + 15) + (S + 15) = 120
Solve for S.
I hope this helps. Thanks for asking
To solve this problem, let's start by assigning variables to represent the side lengths of the triangle. Since it is mentioned that one side is 15 cm shorter than the other two sides, let's assume that the length of the two equal sides is x cm. Therefore, the length of the third side would be (x - 15) cm.
Now, the perimeter of a triangle is the sum of its three sides. We are given that the perimeter is 120 cm, so we can set up the equation:
x + x + (x - 15) = 120
Simplifying the equation, we get:
3x - 15 = 120
Next, let's isolate the variable by moving the constant term to the other side:
3x = 120 + 15
3x = 135
Finally, divide both sides of the equation by 3 to solve for x:
x = 135 / 3
x = 45
Now that we have the value of x, we can find the lengths of the three sides of the triangle:
- The two equal sides: x cm = 45 cm
- The shorter side: (x - 15) = (45 - 15) = 30 cm
Therefore, the lengths of the sides of the isosceles triangle are 45 cm, 45 cm, and 30 cm.