A rectangular sheet has an area equal to a square plot. If the sheet measures 72 m in length and 50 m in breadth, and the square plot has an area equal to the sheet, find the perimeter of the square plot.
- (a)112 m
- (b)120 m
- (c)240 m
- (d)220 m
Answer
Why
Correct — C. Equal area is the link between the two shapes.
Area of the sheet: 72 × 50 = 3600 m²
Side of the square: √3600 = 60 m
Perimeter of the square: 4 × 60 = 240 m → option (c)
Check: 60 × 60 = 3600 m², the same as the sheet.
Why the others are wrong
- (a)112 m — A 112 m perimeter means a side of 28 m and an area of 784 m², far below the sheet's 3600 m².
- (b)120 m — 120 m is 2 × 60, two sides of the square instead of four. A 120 m perimeter means a side of 30 m and an area of 900 m².
- (d)220 m — A 220 m perimeter means a side of 55 m and an area of 3025 m², which falls 575 m² short of 3600 m².
Concept
Two shapes with equal area can have different perimeters, so the working passes through the area, never through the perimeter.
From the area, the square's side is its square root, and the perimeter is 4 × side.
The sheet's own perimeter is 2(72 + 50) = 244 m, while the square's is 240 m. Among rectangles of equal area, the square has the smallest perimeter.
72 × 50 = 3600 is a perfect square, 60², which is why the side and the perimeter come out whole.
Key facts
- Area of a rectangle = length × breadth.
- Area of a square = side², so side = √area and perimeter = 4 × √area.
- Among rectangles of equal area, the square has the smallest perimeter.
Study next
Common traps
- Computing the sheet's perimeter, 2(72 + 50) = 244 m: equal area does not mean equal perimeter.
- Stopping at the side, 60 m, or doubling it to 120 m instead of multiplying by 4.
Here an area is carried from a rectangle to a square and a perimeter is asked. Going from a square's area to its side and then to a perimeter also decides 24 Sep 2025, 16:00, Quant Q.9 (a 225 cm² tile cut into two rectangles).
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