To find the value of $y$, we will apply the Pythagorean theorem, which is used for right triangles. The theorem states:

$a^2 + b^2 = c^2$

Where:

• $c$ is the hypotenuse (the longest side, opposite the right angle),
• $a$ and $b$ are the other two sides.

Here:

• $c = 14 \, \text{cm}$ (hypotenuse),
• $b = 7 \, \text{cm}$,
• $y$ is the unknown side we need to find.

Step-by-Step Solution:

1. Write the Pythagorean theorem: $y^2 + 7^2 = 14^2$

2. Substitute the given values: $y^2 + 49 = 196$

3. Solve for $y^2$ by subtracting $49$ from $196$: $y^2 = 196 - 49$ $y^2 = 147$

4. Take the square root of both sides to find $y$: $y = \sqrt{147}$

5. Use a calculator to approximate: [ y \approx 12