The area of a rectangular field with length $90 ext{ m}$ and breadth $80 ext{ m}$ is equal to the area of a square plot. What is the length of the diagonal of the square plot?

Question

The area of a rectangular field with length $90 	ext{ m}$ and breadth $80 	ext{ m}$ is equal to the area of a square plot. What is the length of the diagonal of the square plot?

Accepted Answer

**Solution:**

1. Calculate the area of the rectangular field:
   - Area = length $	imes$ breadth = $90 	imes 80 = 7200 	ext{ m}^2$

2. Since the square plot has the same area, let the side of the square be $s$:
   - $s^2 = 7200$
   - $s = \sqrt{7200} = \sqrt{72 	imes 100} = 10 \sqrt{72} = 10 	imes 6 \sqrt{2} = 60 \sqrt{2} 	ext{ m}$

3. The diagonal $d$ of the square is given by:
   - $d = s \sqrt{2} = 60 \sqrt{2} 	imes \sqrt{2} = 60 	imes 2 = 120 	ext{ m}$

**Answer:** $120 	ext{ m}$

Answer

Answer

Answer

Answer