1. **State the problem:** We have a right-angled triangle with hypotenuse length $b$ cm and other sides $f$ cm and $g$ cm. 2. **Write down the formula connecting $f$, $g$, and $b$:** By the Pythagorean theorem, the square of the hypotenuse equals the sum of the squares of the other two sides: $$b^2 = f^2 + g^2$$ 3. **Make $f$ the subject of the formula:** Rearrange the formula to solve for $f^2$: $$f^2 = b^2 - g^2$$ Taking the positive square root (since length is positive): $$f = \sqrt{b^2 - g^2}$$ 4. **Find $f$ when $g = 2$ cm and $b = 2.5$ cm:** Substitute the values: $$f = \sqrt{(2.5)^2 - (2)^2} = \sqrt{6.25 - 4} = \sqrt{2.25}$$ Calculate the square root: $$f = 1.5$$ **Final answer:** $f = 1.5$ cm