Question

The length of eachof the two congruent sides of an isosceles triangle is 2x +3. The length of the third side is 2x. It's perimeter is 36 centimeters. Draw and label this triangle. Write an equation that could be used to find the value of x. Solve for x and then find the length of all three sides

Answer 1

x = 5

The length of all three sides = 13cm

Explanation:

The length of each of the two congruent sides of an isosceles triangle is,

2x +3.

The length of the third side is 2x.

Its perimeter is 36 centimeters.

As we know the formula of the perimeter of an isosceles triangle,

Perimeter = 2 ( sides length ) + ( length of the third side ),

By putting data in the formula,

Perimeter=2(sides length)+(length of third side)

36cm = 2 ( 2x +3 ) + ( 2x ), 36cm = 4x + 6 + 2x, 6x + 6 = 36cm, 6x = 30,

as x = 5cm,

The length of each of the two congruent sides of an isosceles triangle is,

2x + 3 = 2 ( 5 ) + 3 = 13cm,

The length of the third side is 2x = 2 ( 5 ),

=> 2x = 10

=> x = 10 / 2

=> x = 5