Question

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

Answer 1

Hint: An isosceles triangle is a triangle which has two equal sides and the perimeter of a triangle is called the sum of all the sides of the triangle. Use both the properties to reach the answer.

Complete step-by-step answer:
Given that the triangle is an isosceles triangle and its two equal sides are $3x - 1$ and $2x + 2$ units
So,
\[
   \Rightarrow 3x - 1 = 2x + 2 \\
   \Rightarrow 3x - 2x = 2 + 1 \\
   \Rightarrow x = 3 \\
\]
Therefore, the value of \[x\] is 3.
As we know that the perimeter of triangle = sum of its all sides
The sides of the given triangles are $3x - 1$ , $2x + 2$ and $2x$
Therefore the perimeter of triangle
$
   = 3x - 1 + 2x + 2 + 2x \\
   = 7x + 1 \\
 $
Substituting value of $x$ in above equation, we have
Perimeter of triangle
$
   = 7 \times 3 + 1 \\
   = 22{\text{ units}}{\text{.}} \\
$
Thus \[x = 3\] and the perimeter of the triangle is 22 units.

Note: To solve problems related to finding the value of x and the perimeter of a polygon. First find the conditions given the question and using those conditions the value of x can be found. Second, in order to find the perimeter of the polygon whether it is a triangle, square, hexagon etc. take the sum of all sides of the polygon. But in case of a circle the perimeter is $2\pi r$ ; where r is the radius of the circle.