one of the equal sides of an isoceles triangle is 3m less than twice its base. The perimeter is 44m. Find the length of the sides. The teacher gave us the answer of 17m for the two sides and 10 for the base. What formula did he use to find this.

Let x = length of base

Perimeter = sum of sides

44 = 2(2x-3) + x

Solve for x, then 2x -3.

To solve this problem, the teacher likely used the concept of an isosceles triangle and applied the perimeter formula. Let's break down the problem and solve it step by step.

Given:
- One of the equal sides of the isosceles triangle is 3m less than twice its base.
- The perimeter of the triangle is 44m.

Let's assume the length of the base is 'x'.

According to the problem, one of the equal sides is 3m less than twice the base, which can be expressed as (2x - 3).

Since it is an isosceles triangle, the other equal side's length will also be (2x - 3).

The perimeter of a triangle is the sum of all its side lengths, so we can set up an equation to represent this:

Base + Equal Side + Equal Side = Perimeter
x + (2x - 3) + (2x - 3) = 44

Now, let's solve the equation:

x + (2x - 3) + (2x - 3) = 44
5x - 6 = 44
5x = 50
x = 10

So, the base length is 10m.

Now, substituting the value of x back into the expressions for the equal side lengths:

Equal Side = (2x - 3)
Equal Side = (2 * 10 - 3)
Equal Side = 17

Therefore, the length of the equal sides is 17m.

In conclusion, based on the given information, the teacher used the perimeter formula and the fact that an isosceles triangle has two equal sides to find the side lengths of 17m for each equal side and 10m for the base.