Question

The square below has an area of 1+2x+x^2 square meters. What expression represents the length of one side of the square?

Answer 1

Side length = x + 1 meters

Explanation:

`x^2+2x+1=x^2+2(x)(1)+1^2\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\=(x+1)^2\\\\\text{The formula os an area of a square with side}\ a:\\\\A=a^2\\\\\text{Conclusion:}\\\\Side\ length=x+1`

Answer 2

We have been given that the square has an area of
`1+2x+x^2` square meters. We are asked to find the length of one side of the square.

We know that area of square is square of its side length.

Let us factor area by splitting the middle term.

`x^2+2x+1`

`x^2+1x+1x+1`

`x(x+1)+1(x+1)`

`(x+1)(x+1)`

`(x+1)^2`

To find side length, we will take positive square root of area as:

`√((x+1)^2)`

Square root will cancel out with square, so we will get:

`√((x+1)^2)=(x+1)`

Therefore, the length of the one side of the square in (x+1) meters.