Question

A diagonal of a square measures 10 units. What is the length of one of its sides?

Answer 1

Given Data:

The length of the diagonal of the squre is:d=10 units.

Let 'a' be the length of a side of the given square.

The expression to caclculate the length of the side 'a' is,

`\begin{gathered} d=\sqrt[]{a^2+a^2} \\ d=\sqrt[]{2a^2} \\ a=\sqrt[]{(d^2)/(2)} \end{gathered}`

Substitute values in the above expression.

`\begin{gathered} a=\sqrt[]{(10^2)/(2)} \\ a=\sqrt[]{(100)/(2)} \\ a=\sqrt[]{50} \\ a=5\sqrt[]{2} \\ a=7.071\text{ units} \end{gathered}`

Thus, the length of the side a is 7.071 units.