width of the veranda if its area is to be \( 24 \mathrm{~m}^{2} \), 10 A father's age is the square of his son's age \( (x) \), In 20 years' time the father will be three times as old as his son. What are the ages of the father and son?

To find the dimensions of the veranda, you can start from the area formula for rectangles: \( \text{Area} = \text{Length} \times \text{Width} \). If we assume the length to be a fixed value and the area is \( 24 \mathrm{~m}^{2} \), you can easily find the corresponding width by rearranging the formula. For example, if the length is \( 6 \mathrm{~m} \), the width would be \( \frac{24}{6} = 4 \mathrm{~m} \). Play around with various lengths to see how the width changes! Now, moving on to the ages: Let’s denote the son’s age as \( x \). According to the problem, the father's age is \( x^2 \). In 20 years, the son's age will be \( x + 20 \) and the father's age will be \( x^2 + 20 \). The equation becomes \( x^2 + 20 = 3(x + 20) \). Simplifying that leads to a quadratic equation. Solving it will give you both the father’s and son’s current ages!