Question

A rectangle is (x + 6) meters long and (2x – 1)meters wide. Find the area of the rectangle in squaremeters.

Answer 1

Recalling the formula for calculating the area of a rectangle:

$Area=base\times height$

Since the base is equal to (x+6) meters and the height is equal to (2x-1) (it actually doesn't matter which is the height and which is the base), then:

$Area=(x+6)\cdot(2x-1)$

Use the distributive property two times to rewrite the expression in terms of x:

$\begin{gathered} (x+6)(2x-1)=x\cdot(2x-1)+6\cdot(2x-1) \\ =x\cdot2x-x\cdot1+6\cdot2x-6\cdot1 \end{gathered}$

Use additional properties of multiplication and addition to further simplify the expression:

$\begin{gathered} x\cdot2x-x\cdot1+6\cdot2x-6\cdot1 \\ =2x^2-x+12x-6 \\ =2x^2+11x-6 \end{gathered}$

Therefore, the area of the rectangle is 2x^2+11x-6 square meters.