The perimeter of an isosceles obtuse triangle is 90 cm, one of its sides is 18 cm larger

The perimeter of an isosceles obtuse triangle is 90 cm, one of its sides is 18 cm larger than the other. Find the sides of the triangle

According to the definition of an isosceles obtuse-angled, its two sides are equal.

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

Then the length of the second lateral side of this triangle should also be equal to x.

According to the condition of the problem, one of the sides of this triangle is 18 cm larger than the other.

Let’s consider 2 cases.

1) the lateral side is 18 cm larger than the base.

Then the length of the base should be equal to x – 18 cm and since the perimeter of the triangle is 90 cm, we can draw up the following equation:

x + x + x -18 = 90,

solving which, we get:

3x – 18 = 90;

3x = 18 + 90;

3x = 108;

x = 108/3 = 36.

Therefore, the lengths of the sides of this triangle should be equal to 36 cm, 36 cm and 18 cm.

Such a triangle is acute-angled and does not satisfy the condition of the problem.

1) the lateral side is 18 cm less than the base.

Then the length of the base should be equal to x + 18 cm and since the perimeter of the triangle is 90 cm, we can draw up the following equation:

x + x + x + 18 = 90,

solving which, we get:

3x + 18 = 90;

3x = 90 – 18;

3x = 72;

x = 72/3 = 24. to

Therefore, the lengths of the sides of this triangle should be equal to 24 cm, 24 cm and 42 cm.

Such a triangle is obtuse and satisfies the condition of the problem.

Answer: 24 cm, 24 cm and 42 cm.