Development Area
1. **State the problem:**
We want to find the area of a right triangle with legs each measuring $\frac{1}{2}$ mile and compare it to the total area of 50 football pitches.
2. **Convert units:**
One mile equals 1600 meters.
Therefore, $\frac{1}{2}$ mile = $\frac{1}{2} \times 1600 = 800$ meters.
3. **Calculate the area of the triangle:**
The area of a right-angled triangle is given by:
$$\text{Area} = \frac{1}{2} \times \text{leg}_1 \times \text{leg}_2$$
Substituting:
$$\text{Area} = \frac{1}{2} \times 800 \times 800 = \frac{1}{2} \times 640000 = 320000 \text{ m}^2$$
4. **Calculate the area of one football pitch:**
Each pitch measures 100 m by 50 m.
Area = $100 \times 50 = 5000$ m$^2$
5. **Calculate the total area of 50 football pitches:**
$$50 \times 5000 = 250000 \text{ m}^2$$
6. **Compare the areas:**
Area of development = 320000 m$^2$
Area of 50 pitches = 250000 m$^2$
Since $320000 > 250000$, the development area is greater.
**Final answer:**
The area of the development ($320000$ m$^2$) is greater than the total area of 50 football pitches ($250000$ m$^2$).