The perimeter of an isosceles triangle is 15cm, and one of its sides is 4cm less than the other

The perimeter of an isosceles triangle is 15cm, and one of its sides is 4cm less than the other. Find the sum of the sides of this triangle.

Since this triangle is isosceles, its two sides are equal.

Let x denote the length of the lateral side of this triangle.

Then the length of the other side of this triangle is also x cm.

It is known from the problem statement that one of the sides of this triangle is 4 cm smaller than the other.

Let’s consider two possible cases.

1) The lateral side of this triangle is 4 cm less than its base.

Then the length of the base should be equal to x + 4 cm, and since the perimeter of this triangle is 15 cm, we can draw up the following equation:

x + x + x + 4 = 15,

solving which, we get:

3x + 4 = 15;

3x = 15 – 4;

3x = 11;

x = 11/3 cm.

Then the sum of the sides of this triangle is 2 * 11/3 = 22/3 = 7 1/3.

2) The lateral side of this triangle is 4 cm larger than its base.

Then the length of the base should be equal to x – 4 cm, and since the perimeter of this triangle is 15 cm, we can draw up the following equation:

x + x + x – 4 = 15,

solving which, we get:

3x – 4 = 15;

3x = 15 + 4;

3x = 19;

x = 19/3 cm.

Then the sum of the sides of this triangle is 2 * 19/3 = 38/3 = 12 2/3.

Answer: 7 1/3 cm or 12 2/3 cm.