# The lengths of the sides of a triangle are 3x, 5x - 12, and x + 20. Find the value of x so that the triangle is isosceles?

**Solution:**

An __isosceles triangle__ is one in which the two sides of a triangle are equal in length.

The three sides given are 3x, 5x - 12 and x + 20.

The three possibilities are:

(1) 3x = 5x - 12

(2) 3x = x + 20

Or

(3) 5x - 12 = x + 20

From (1) we have

3x = 5x - 12

12 = 5x - 3x

12 = 2x

x = 6

The sides are then 18, 18 and 26

From (2) we have

3x = x + 20

2x = 20

x = 10

The three sides are then 30, 38 and 30

From (3) we have

5x - 12 = x + 20

4x = 32

x = 8

The three sides are then 24, 28, 28

## The lengths of the sides of a triangle are 3x, 5x - 12, and x + 20. Find the value of x so that the triangle is isosceles?

**Summary:**

The lengths of the sides of a triangle are 3x, 5x - 12, and x + 20. The value of x so that the triangle is isosceles is 8, 6 or 10

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