1. **Write 1.52 as an improper fraction in simplest form.** Step 1: Express 1.52 as a fraction. $$1.52 = \frac{152}{100}$$ Step 2: Simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD). The GCD of 152 and 100 is 4. $$\frac{\cancel{152}^{38}}{\cancel{100}^{25}} = \frac{38}{25}$$ So, 1.52 as an improper fraction in simplest form is $\frac{38}{25}$. 2. **Work out 60 as a percentage of 20.** Step 1: Use the formula for percentage: $$\text{Percentage} = \left(\frac{\text{part}}{\text{whole}}\right) \times 100$$ Step 2: Substitute the values: $$\left(\frac{60}{20}\right) \times 100 = 3 \times 100 = 300$$ So, 60 is 300% of 20. 3. **Use Pythagoras' theorem to work out the value of $x$.** Step 1: State the problem. We have a right-angled triangle with hypotenuse 17.2 cm, one leg 12.9 cm, and the other leg $x$. Step 2: Recall Pythagoras' theorem: $$\text{hypotenuse}^2 = \text{leg}_1^2 + \text{leg}_2^2$$ Step 3: Substitute known values: $$17.2^2 = 12.9^2 + x^2$$ Step 4: Calculate squares: $$295.84 = 166.41 + x^2$$ Step 5: Isolate $x^2$: $$x^2 = 295.84 - 166.41 = 129.43$$ Step 6: Find $x$ by taking the square root: $$x = \sqrt{129.43} \approx 11.38$$ So, $x \approx 11.38$ cm.