Four top rectangles match five bottom ones in length, giving 4l = 5b, so l = 5b/4. Area 9lb = 72 yields lb = 8. Solving gives b = 2.53 cm, l = 3.16 cm, and perimeter ≈ 11.38 cm.
The figure shows nine identical rectangles fitted together to make a large rectangle whose area is 72 cm². Find the perimeter of each small rectangle.
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Let the length and breadth of each identical small rectangle be l and b.
From Fig. 6.47, the top row has 4 rectangles placed lengthwise and the bottom row has 5 rectangles placed lengthwise along the same total width:
4l = 5b (or 4 of one dimension equals 5 of the other).
Thus, l = 1.25b.
The total area of nine identical rectangles is 72 cm²:
9 x (l x b) = 72, which gives l x b = 8 cm².
Substitute l = 1.25b:
1.25b² = 8, so b² = 6.4, giving b = √6.4 ≈ 2.53 cm.
Then l = 8 / 2.53 ≈ 3.16 cm.
Perimeter of each small rectangle = 2(l + b) = 2(3.16 + 2.53) = 2(5.69) ≈ 11.38 cm.
For more NCERT Solutions of Class 9 Ganita Manjari Chapter 6 Measuring Space: Perimeter and Area Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-6/