The rectangle below has an area of x^2+13x+36 square meters and a length of x+9 meters what expression represents the width of the rectangle

Answer 1

We know that the area of a rectangle can be found by multiplying (length)(width)

The length in this question is already given as (x + 9) and the area is given as (x^2 + 13x + 36), so we need to find an equation for the width that will give us the area.

When I see a quadratic equation, one with the x^2, I always wonder if it can be factored. In this case, it can be factored. The factored equation becomes (x + 9)(x + 4).

We can now think of the area as these two expressions being multiplied together. If you look carefully at the factored area, you can see that one of the terms here is the same as the length!

Because of this, as the area is (length * width), the width is the other term in the area, so it is (x + 4).