two equal sides of an isosceles triangle are (3x-1)and (2x+2) units . third sides is 2x units . finds x and the perimeter of the triangle
If the two sides are equal, then:
3x-1 = 2x+2
Solve for x and then add the three sides.
To find the value of x and the perimeter of the triangle, we need to apply the properties of an isosceles triangle.
In an isosceles triangle, two sides are equal in length. Let's set up an equation using this information.
We are given two equal sides: (3x - 1) and (2x + 2). Therefore, we can equate them using the equation:
3x - 1 = 2x + 2
Now, let's solve the equation to find the value of x.
3x - 2x = 2 + 1
x = 3
Now that we have found the value of x, we can substitute it back into the given sides to find their lengths.
For the first side: (3x - 1) = (3 * 3 - 1) = 8 units
For the second side: (2x + 2) = (2 * 3 + 2) = 8 units
For the third side: 2x = 2 * 3 = 6 units
Now, we can calculate the perimeter of the triangle by adding the lengths of all three sides.
Perimeter = (8 + 8 + 6) = 22 units
Therefore, the value of x is 3, and the perimeter of the triangle is 22 units.