Rectangular field length 8 m, breadth 2 m. Square field has same perimeter. Find which has greater area.
Step 1: Find the perimeter of the rectangle.
Perimeter formula: \( P = 2 \times (\text{length} + \text{breadth}) \)
\( P = 2 \times (8 + 2) \)
\( P = 2 \times 10 \)
\( P = 20\,\text{m} \)
Step 2: Square has the same perimeter, so find its side.
Perimeter of a square: \( 4 \times \text{side} = 20 \)
\( \text{side} = \dfrac{20}{4} \)
\( \text{side} = 5\,\text{m} \)
Step 3: Find the area of the rectangle.
Area formula: \( A = \text{length} \times \text{breadth} \)
\( A_{\text{rect}} = 8 \times 2 \)
\( A_{\text{rect}} = 16\,\text{m}^2 \)
Step 4: Find the area of the square.
Area formula: \( A = \text{side} \times \text{side} \)
\( A_{\text{sq}} = 5 \times 5 \)
\( A_{\text{sq}} = 25\,\text{m}^2 \)
Step 5: Compare areas.
\( 25\,\text{m}^2 \gt 16\,\text{m}^2 \Rightarrow \) the square field has a greater area.