Question

find the length of side x to the nearest tenth.

Explanation:

Step1: Identify the right - triangle

This is a right - triangle with legs of length 3 and 3 (since the two sides adjacent to the right - angle are equal as indicated by the tick marks).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem for a right - triangle is $a^{2}+b^{2}=c^{2}$, where $a$ and $b$ are the legs and $c$ is the hypotenuse. Here $a = 3$, $b = 3$, and $c=x$. So, $x=\sqrt{3^{2}+3^{2}}$.

Step3: Calculate the value of $x$

First, calculate $3^{2}+3^{2}=9 + 9=18$. Then $x=\sqrt{18}$. Simplify $\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}\approx3\times1.414 = 4.242$. Rounding to the nearest tenth, $x\approx4.2$.

Answer:

$4.2$