Given the area of the rectangle is given by the following expression:
[tex]A=x^2+5x+6[/tex]
The area of the rectangle is the product of the length by the width
So, we will factor the given expression
To factor the expression, we need two numbers the product of them = 6
and the sum of them = 5
So, we will factor the number 6 to find the suitable numbers
6 = 1 x 6 ⇒ 1 + 6 = 7
6 = 2 x 3 ⇒ 2 + 3 = 5
So, the numbers are 2 and 3
The factorization will be as follows:
[tex]A=(x+3)(x+2)[/tex]
So, the answer will be the possible dimensions are:
[tex]\begin{gathered} \text{Length}=x+3 \\ \text{Width}=x+2 \end{gathered}[/tex]
