Perimeter of an isosceles triangle is 50 cm. If one of the two equal sides is 18 cm, find the third side.
Third side of the triangle = 14 cm
Step-by-step solution
Given: The triangle is isosceles, so it has two equal sides.
Perimeter = 50 cm
Each equal side = 18 cm
Recall the formula for perimeter of a triangle:
\( \, \text{Perimeter} = \text{side}_1 + \text{side}_2 + \text{side}_3 \, \)
Here: \( \, \text{Perimeter} = 18 + 18 + \text{base} \, \)
Add the two equal sides:
\( \, 18 + 18 = 36 \, \)
Set up the equation using the given perimeter:
\( \, 50 = 36 + \text{base} \, \)
Solve for the base (third side):
\( \, \text{base} = 50 - 36 \, \)
\( \, \text{base} = 14\ \text{cm} \, \)
Quick check:
\( \, 18 + 18 + 14 = 50\ \text{cm} \, \) ✔️