Question:
Find the length of a side of a sqiare, whose area is equal to the area of a rectangle with sides 240 m and 70 m.
Solution:
The area of the rectangle $=240 \mathrm{~m} \times 70 \mathrm{~m}=16800 \mathrm{~m}^{2}$
Given that the area of the square is equal to the area of the rectangle.
Hence, the area of the square will also be 16800 m2.
The length of one side of a square is the square root of its area.
$\therefore \sqrt{16800}=\sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 5 \times 5 \times 7}$
$=2 \times 2 \times 5 \sqrt{2 \times 3 \times 7}$
$=20 \sqrt{42} \mathrm{~m}=129.60 \mathrm{~m}$
Hence, the length of one side of the square is 129.60 m