Question

solve for x. round to the nearest tenth if necessary.
right triangle with legs 3, hypotenuse x
options:
○ x = 9
○ x = 18
○ x = 5.3
○ x = 4.2
○ x = 3.3

Explanation:

Step1: Identify the triangle type

The triangle is a right - isosceles triangle with legs \(a = 3\) and \(b=3\), and hypotenuse \(x\). We use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\) (where \(c\) is the hypotenuse and \(a,b\) are the legs of the right triangle).

Step2: Apply the Pythagorean theorem

Substitute \(a = 3\) and \(b = 3\) into the formula:
\[

$$\begin{align*} x&=\sqrt{3^{2}+3^{2}}\\ &=\sqrt{9 + 9}\\ &=\sqrt{18}\\ &=\sqrt{9\times2}\\ & = 3\sqrt{2}\\ &\approx3\times1.414\\ &\approx4.242\approx4.2 \end{align*}$$

\]

Answer:

\(x = 4.2\) (the option with \(x = 4.2\))