Question

The two equal sides of an isosceles triangle each have a length of 2x + 3y - 1. The perimeter of the triangle is 7x + 9y. Determine the length of the third side.

Answer 1

To find the length of the third side, substitute the values of x and y into the expression and simplify.

Step-by-step explanation:

To find the length of the third side of an isosceles triangle, we need to first determine the value of x and y. Then, we can substitute these values into the expression for the length of the third side.

Given that the two equal sides of the triangle have a length of 2x + 3y - 1, and the perimeter is 7x + 9y, we can set up the equation:

2(2x + 3y - 1) + 2x = 7x + 9y

Simplifying the equation, we get:

4x + 6y - 2 + 2x = 7x + 9y

Combining like terms, we have:

6x + 6y - 2 = 7x + 9y

Now, let's isolate the x's and y's on opposite sides of the equation:

6x - 7x = 9y - 6y + 2

-x = 3y + 2

x = -3y - 2

Now that we have the value of x in terms of y, we can substitute this into the expression for the length of the third side:

Length of third side = 2x + 3y - 1

Length of third side = 2(-3y - 2) + 3y - 1

Length of third side = -6y - 4 + 3y - 1

Length of third side = -3y - 5

So, the length of the third side is -3y - 5.