1. **State the problem:** A photograph measures 7 $\frac{1}{2}$ cm (which is 7.5 cm) by 5 cm. It is enlarged so that the longer side becomes 24 cm. We need to find the length of the shorter side after enlargement. 2. **Identify the formula:** The enlargement keeps the aspect ratio the same, so the ratio of the sides remains constant. This means: $$\frac{\text{original longer side}}{\text{original shorter side}} = \frac{\text{new longer side}}{\text{new shorter side}}$$ 3. **Apply the known values:** Original longer side = 7.5 cm Original shorter side = 5 cm New longer side = 24 cm New shorter side = $x$ cm (unknown) 4. **Set up the proportion:** $$\frac{7.5}{5} = \frac{24}{x}$$ 5. **Solve for $x$:** Multiply both sides by $x$: $$7.5 \times x = 5 \times 24$$ $$7.5x = 120$$ Divide both sides by 7.5: $$x = \frac{120}{7.5}$$ $$x = 16$$ 6. **Interpretation:** The length of the shorter side after enlargement is 16 cm. **Final answer:** 16 cm