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

Find the length of the 3rd side using the simplest radical form-example-1

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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*25} \\ c=\sqrt[]{2}*\sqrt[]{25} \\ c=5\sqrt[]{2} \end{gathered}

ANSWER:

The third side of the triangle would now be;


5\sqrt[]{2}

User RexBarker
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