Question

A square has an area of 16j^2 + 24j + 9. How can you find the length of the side of the square?

Answer 1

first off let's recall that a square has all equal sides, so its area is just one side squared, namely A = s², or A = (s)(s).

we know the area is 16j² + 24j + 9, that simply means that two twin factors are in it, and it also means that the area polynomial is a perfect square trinomial.

$\bf \qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2 \\\\[-0.35em] ~\dotfill\\\\ 16j^2+24j+9\implies 4^2j^2+2(4j)(3)+3^2\implies (4j)^2+2(4j)(3)+3^2 \\\\\\ (4j+3)^2\implies \stackrel{\textit{area}}{(4j+3)(4j+3)}~\hspace{7em} \stackrel{\textit{one side}}{4j+3}$