Trust your identities 3

Algebra Level 2

As shown on the diagram above, the area of a square , in terms of $x$ , is $9x^{2} + 12x + 4$ .

Find the length of its side in terms of $x$ .

Suggestion: Try to solve it without using the choices given.

3x+2

Cannot be determined

3x^{2}+2

3x+6

1 solution

Ethan Mandelez
Mar 31, 2021

Consider the identity

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

Since we know that $9x^{2} + 12x + 4$ is in the form $(a+b)^{2}$ , we can expand the brackets and equate:

$a^{2} = 9x^{2}$ which leads to $a = 3x$

$b^{2} = 4$ which leads to $b = 2$

$2ab = 2 \times 3x \times 2 = 12x$

Therefore, the side of the square is $3x + 2$ .