The difference in the lengths of the two sides of an isosceles triangle

The difference in the lengths of the two sides of an isosceles triangle is 12 cm, and the perimeter of the triangle is 48 cm. What are the sides of the triangle?

The perimeter and the difference in the sizes of the sides in an isosceles triangle are known. Find the lengths of the sides of the triangle.

To begin with, we note the fact that we are talking about the difference in the lengths of the side and the base, since there simply cannot be a difference in the lengths of equal sides.

Let x be the length of the side of the triangle, then (x – 12) is the length of the base of the triangle. Let’s write our equation:

x + x + (x – 12) = 48;

3 * x = 60;

x = 20 cm.

x – 12 = 8 cm.

Lateral side – 20 cm, base – 8 cm.

If the base is greater than the lateral length, then:

x + x + x + 12 = 48;

x = 12;

x + 12 = 24.

Lateral side – 12 cm, base – 24 cm.