The perimeter of an isosceles triangle is 84 cm and one of its sides is 12 cm less than the other.

| June 20, 2021 | education

The perimeter of an isosceles triangle is 84 cm and one of its sides is 12 cm less than the other. Find the sides of this triangle.

Let us denote by a the length of the base of this isosceles triangle.

Let’s consider two possible cases.

1) The length of the base of this isosceles triangle is 12 cm less than the length of its lateral side.

Then the lengths of the sides should be equal to a – 12 cm.

Since the perimeter of this isosceles triangle is 84 cm, we can make the following equation:

a + a – 12 + a – 12 = 84,

solving which, we get:

3a – 24 = 84;

(3а – 24) / 3 = 84/3;

a – 8 = 28;

a = 28 + 8 = 36 cm.

We find the length of the side:

a – 12 = 36 – 12 = 24 cm.

2) The length of the base of this isosceles triangle is 12 cm less than the length of its lateral side.

Then the lengths of the sides should be equal to a + 12 cm.

Since the perimeter of this isosceles triangle is 84 cm, we can make the following equation:

a + a + 12 + a + 12 = 84,

solving which, we get:

3a + 24 = 84;

(3a + 24) / 3 = 84/3;

a + 8 = 28;

a = 28 – 8 = 20 cm.

We find the length of the side:

a + 12 = 20 + 12 = 32 cm.

Answer: two triangles satisfy the condition of the problem: 36 cm, 24 cm, 24 cm and 20 cm, 32 cm, 32 cm.



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