Question

What is the length of a diagonal of a square if its area is $98$square feet?

Answer 1

Find the length of a diagonal of a square if its area is $98$square feet.

Apply the area formula to find the side of the square,
Area of a square:

$\begin{array}{rcl}Area& =& {\left(side\right)}^2\\ & \Rightarrow & {\left(side\right)}^2=98\end{array}$
We can use any one of the sides for the calculation because they all have identical magnitudes.

$\begin{array}{rcl}& & {\left(\mathrm{AB}\right)}^2=98\\ & \Rightarrow & \mathrm{AB}=\sqrt{9}8\\ & \Rightarrow & \mathrm{AB}\approx 9.899494937\\ & \Rightarrow & \mathrm{AB}\approx 9.9\\ & & \end{array}$ units.
Because all sides are equal, $AB=BD=CD=AD$
Hence, we know that $\mathrm{AB}\approx 9.9$ and $\mathrm{AC}=9.9$ units Then,
The right triangle $BAC$Pythagoras Theorem :

$\begin{array}{rcl}{\left(BC\right)}^2& =& {\left(AC\right)}^2+{\left(AB\right)}^2{\left(BC\right)}^2=9.92+9.92\end{array}$
By using the calculator,

$\begin{array}{rcl}{\left(BC\right)}^2& =& 98.01+98.01{\left(BC\right)}^2\\ & =& 196.02BC\\ & =& \sqrt{196.02}\end{array}$

$$\begin{gathered} \Rightarrow BC=14.00071427 \\ \Rightarrow BC\approx 14.0 \end{gathered}$$
Therefore, the diagonal length $\left(BC\right)$ is nearly$14$ feet.