Question

A rectangle has an area ofx2+ 10x + 21Find the expressions that represent the dimensions of the rectangle.O (x - 3) and (x + 7)O (x + 1) and ( x + 21)O 3 and 7O (x + 3) and ( x + 7)

Answer 1

The expressions that represent the dimensions of the rectangle are:

(x+3) and (x+7)

Step-by-step explanation:

The area of the said rectangle is

`x^2+10x+21`

To find an expression that represents the dimensions of the rectangle, we need to factorize the expression for the area.

`\begin{gathered} x^2+10x+21 \\ =x^2+3x+7x+21 \\ =(x^2+3)+(7x+21) \\ =x(x+3)+7(x+3) \\ =(x+3)(x+7) \end{gathered}`

Therefore, the expressions we are looking for are

(x+3) and (x+7)