Question

The length of a side of a square is (2x + 1) km. Find the area of thesquare in terms of the variable x

Answer 1

The area of the square is given by:

$A=s^2$

Where s is the length of the side. Then s=(2x+1) km.

By replacing this into the formula we have:

$A=(2x+1)^2$

Also, the square of a sum is given by:

$(a+b)^2=a^2+2ab+b^2$

If a=2x and b=1, then:

$\begin{gathered} (2x+1)^2=(2x)^2+2(2x)(1)+(1)^2 \\ (2x+1)^2=4x^2+4x+1 \end{gathered}$

Thus, the area of the square in terms of the variable x is:

$A=4x^2+4x+1$