Question

The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Write two equations which represent the two sentences.
Solve the system you wrote for this using any technique.

Answer 1

The perimeter of a triangle is just equal to the sum of the measures of the sides. Since the sides have measures x, x, and y, we know the perimeter is x+x+y, which is the same as 2x+y. Since the perimeter is equal to 46, our first equation is 2x+y=46.

Since the measure y is 4 centimeters longer than the measure x, we know y is 4 more than x, so the second equation is y=x+4.

So, the two equations are 2x+y=46 and y=x+4.