Question

The length of the base of an isosceles triangle is x. The length of a leg is 3x−6. The perimeter of the triangle is 65. Find x.

Answer 1

x = 11

Explanation:

Hello!

In an isosceles triangle, the two legs are congruent by the property Base angle Theorem. It is isosceles when both angles on the base are congruent.

So, since the base is x, and the measure of one leg is 3x - 6, we know that the other leg is also 3x - 6 in length.

The equation for perimeter is : leg + leg + base = Perimeter

We can plug in 65 for the perimeter because it's given

Solve for x:

• x + 3x - 6 + 3x - 6 = 65
• 7x - 12 = 65
• 7x = 77
• x = 11

The value of x is 11.