The perimeter of an isosceles obtuse triangle is 45 cm. One of the sides is 9 cm larger than the other

The perimeter of an isosceles obtuse triangle is 45 cm. One of the sides is 9 cm larger than the other. Find the sides of the triangle.

A triangle with two sides equal is called isosceles. Equal sides are called lateral, and the third is called the base.

1 case

Let the base of an isosceles triangle be x cm, then the lateral side is (x + 9) cm.The perimeter of a triangle (the perimeter of a triangle is equal to the sum of its three sides) is (x + (x + 9) + (x + 9)) cm or 45 cm . Let’s compose an equation and solve it.

x + (x + 9) + (x + 9) = 45;

x + x + 9 + x + 9 = 45;

3x + 18 = 45;

3x = 45 – 18;

3x = 27;

x = 27: 3;

x = 9 (cm) – base;

x + 9 = 9 + 9 = 18 (cm) – side.

Answer. 9 cm, 18 cm, 18 cm.

2 case

Let the lateral side of an isosceles triangle be x cm, then the base is equal to (x + 9) cm.By the condition of the problem, it is known that the perimeter of the triangle is (x + x + (x + 9)) cm or 45 cm.Let’s make an equation and solve it.

x + x + (x + 9) = 45;

x + x + x + 9 = 45;

3x + 9 = 45;

3x = 45 – 9;

3x = 36;

x = 36: 3;

x = 12 (cm) – side;

x + 9 = 12 + 9 = 21 (cm) – base.

Answer. 12 cm, 12 cm, 21 cm.