Two equal sides of an isosceles triangle are $3 x - 1$ and $2 x + 2$ units. The third side is 2x units. Find x and the perimeter of the triangle.

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3 and 22

4 and 24

5 and 26

6 and 28

answer is A.

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Detailed Solution

Given,
Two equal sides of an isosceles triangle are

3 x - 1

and

2 x + 2

units
Therefore,

3 x - 1 = 2 x + 2

Take the variable one side of the equation while constant terms at the other side of the equation,

3 x - 2 x = 2 + 1

x = 3

Now, triangle’s third side =

2 x

\begin{matrix} = 2 \times 3 \\ = 6 \end{matrix}

Equal sides of triangle,

= 3 x - 1

\begin{matrix} = 3 \times 3 - 1 \\ = 9 - 1 \\ = 8 \end{matrix}

As, the perimeter is the sum of each side of triangle. So, the triangle perimeter

= 8 + 8 + 6

= 22

Thus, value of x is 3 while the perimeter of the triangle is 22.
Option 1 is correct.

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