Question

3
step 1: \\( \frac { \text { short } } { \text { long } } = \frac { \text { short } } { \text { long } } \\)
step 2: \\( \frac { 3 } { x } = \frac { 1 } { \sqrt { 2 } } \\)
step 3: \\( 3 \sqrt { 2 } = 1 \cdot x \\)
step 4: \\( 3 \sqrt { 2 } = x \\)
step 5: \\( 4.2 \text { units } \approx x \\)

Explanation:

Step1: Set up proportion

$$\frac{\text{short}}{\text{long}}=\frac{\text{short}}{\text{long}}$$

Step2: Substitute values

$$\frac{3}{x}=\frac{1}{\sqrt{2}}$$

Step3: Cross - multiply

$$3\sqrt{2}=1\cdot x$$

Step4: Simplify

$$x = 3\sqrt{2}$$

Step5: Approximate

$$x\approx4.2$$

Answer:

$$x\approx4.2$$