In an isosceles triangle, the perimeter is 36 cm. 1) Find: a) the length of the side if the base is 10 cm;

In an isosceles triangle, the perimeter is 36 cm. 1) Find: a) the length of the side if the base is 10 cm; b) the base if the side is 15 cm. 2) Find the two sides of the triangle if the third side is 14 cm. Hint. In task 2, consider two options.

Perimeter of an isosceles triangle = 36 cm

1)

a) The perimeter is the sum of the lengths of the sides of the triangle. In an isosceles triangle, the sides are equal, we denote them by x. Then, knowing that the base = 10 cm, we will compose the equation:

x + x + 10 = 36

2x = 36 – 10

2x = 26

x = 26/2 = 13 (cm) – the length of the side.

b) Let x be the base, knowing that the side is 15 cm, we get the equation:

x + 15 + 15 = 36

x = 36 – 30 = 6 (cm) – base length.

2) Since it is not indicated which side is 14 cm, it can be both the side and the base. Let’s consider both options.

Option 1, when the base = 14 cm, x is the side:

x + x + 14 = 36

2x = 36 – 14

2x = 22

x = 22/2 = 11 (cm) – side.

Answer: 14 cm and 11 cm.

Option 2, when the side = 14 cm, x is the base:

x + 14 + 14 = 36

x = 36 – 28 = 8 (cm) – base.

Answer: 14 cm and 8 cm.