Question

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.

Write an equation that could be used to find the value of x.


Solve for x.


Then, find the length of all three sides.

Answer 1

`\huge\boxed{\sf x = 5}`

Explanation:

In an isosceles triangle,

Each of two equal sides = 2x + 3

Third side = 2x

Perimeter = 36

We know that,

Perimeter = Sum of all sides

So,

36 = 2x + 3 + 2x + 3 + 2x

• Combine like terms

36 = 2x + 2x + 2x + 3 + 3

36 = 6x + 6

• Subtract 6 from both sides

36 - 6 = 6x

30 = 6x

• Divide both sides by 6

30/6 = x

5 = x

OR

x = 5

Now,

The length of all three sides:

Side 1 and 2:

= 2x + 3

= 2(5) + 3

= 10 + 3

= 13

Side 3:

= 2x

= 2(5)

= 10

`\rule[225]{225}{2}`