Question

Find the expression for the possible length of the rectangle.

Answer 1

We have the next area given:

`A=x^2+5x+6`

Now, we also know that the area of a rectangle is given by:

`A=Lenght\cdot Width`

Then, both expressions must be equal to each other.

`\begin{gathered} x^2+5x+6=Lenght\cdot Width \\ \text{We can factorize the form ax}^2+bx+c \\ \text{ Find two numbers that multiply by each other are equal to 6 and they add up to 5.} \\ \text{Then:} \\ 3\cdot2=6 \\ 3+2=5 \\ \text{Hence}\colon \\ (x+3)(x+2)=Lenght\cdot Width \end{gathered}`

Now, the length expression is (x+3).