71.9k views
3 votes
Find the length of side x in simplest radical form with a rational denominator.45°V545°X

User Jujuleder
by
8.3k points

1 Answer

7 votes

Since we have two angles of 45° and a right angle, we can deduce the opposite and the adjacent side are the same.

Using the pythagoras theorem we have,


\begin{gathered} a^2+b^2=c^2 \\ x^2+x^2=\sqrt[]{5}^2\text{ Adding like terms we have} \\ 2x^2=5\text{ Isolating x, we get.} \\ x^2=(5)/(2)\text{ finding the root we have} \\ x=\sqrt[]{(5)/(2)}=\frac{\sqrt[]{5}}{\sqrt[]{2}} \end{gathered}

Then, we have to find the simplest radical form, with the rational denominator. Rationalizing we have.


\frac{\sqrt[]{5}}{\sqrt[]{2}}=\frac{\sqrt[]{5}}{\sqrt[]{2}}\cdot\frac{\sqrt[]{2}}{\sqrt[]{2}}=\frac{\sqrt[]{5\cdot2}}{\sqrt[]{2\cdot2}}=\frac{\sqrt[]{10}}{\sqrt[]{4}}=\frac{\sqrt[]{10}}{2}

The final answer is


x=\frac{\sqrt[]{10}}{2}

User Yam Tal
by
7.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories