Question

The length of each of the two congruent sides of nan isosceles triangke is 4x+2. The length of the of third side is 2x. The perimeter is 29 centimeters. Write an equation that could be used to find to find the value of x.

Solve for x and find the length of all three sides.

Answer 1

Value of x is 2.5 and the sides are 5 cm, 12 cm and 12 cm.

Explanation:

• Step 1: Given length of the sides of an isosceles triangle = 4x + 2, 4x + 2 and 2x, and perimeter = 29 cm. Write an equation with this data.

Perimeter of a triangle = Sum of its sides

⇒ 29 = 2(4x + 2) + 2x = 8x + 4 + 2x = 10x + 4

⇒ 29 = 10x + 4

⇒ 10x - 25 = 0 is the equation

• Step 2: Solve for x

⇒ 10x = 25

⇒ x = 25/10 = 2.5

• Step 3: Find lengths of the sides

2x = 2 × 2.5 = 5cm

4x + 2 = 4 × 2.5 + 2 = 10 + 2 = 12 cm