Question

Find the length of the 3rd side using the simplest radical form

Answer 1

Given a right angled triangle, we shall solve for the unknown side by applying the Pythagoras' theorem which is;

$c^2=a^2+b^2$

Where c is the hypotenuse (side facing the right angle) and then a and b are the other two sides.

Substituting for the given values, we shall now have the following;

$\begin{gathered} c^2=a^2+b^2 \\ c^2=5^2+5^2 \\ c^2=25+25 \\ c^2=50 \end{gathered}$

Take the square root of both sides;

$\begin{gathered} \sqrt[]{c^2}=\sqrt[]{50} \\ c=\sqrt[]{50} \end{gathered}$

We can now re-arrange the the right side of the equation;

$\begin{gathered} c=\sqrt[]{2\times25} \\ c=\sqrt[]{2}\times\sqrt[]{25} \\ c=5\sqrt[]{2} \end{gathered}$

ANSWER:

The third side of the triangle would now be;

$5\sqrt[]{2}$