Exercise 36
Half the area of a square is \( u^4 \). Then, the length of side is:
-
\( 2 u^2 \)
-
\( u^2 \sqrt{2} \)
-
\( u^2 \)
-
\( u \sqrt{2} \)
-
\( 4 u^2 \)
Try to solve it before checking the answer.
-
\( u^2 \sqrt{2} \)
If \( L \) is the length of the side of the square, its area is \( L^2 \).
Since half of the area is \( u^4 \), we have that:
\[
\begin{aligned}
\frac{L^2}{2} = u^4
&\Rightarrow
L^2 = 2 u^4
\\[.5em]
&\Rightarrow
L = \sqrt{ 2 u^4 }
\\[.5em]
&\hspace{2.5em}
=
\sqrt{2} \sqrt{ u^4 }
\\[.5em]
&\hspace{2.5em}
=
\sqrt{2} u^2
\\[.5em]
&\hspace{2.5em}=
\boldsymbol{ u^2 \sqrt{2} }
\end{aligned}
\]