If the area of a square region having sides of length 6 centimeters is equal…
2025
If the area of a square region having sides of length 6 centimeters is equal to the area of a rectangular region having width 2.5 cm , then the length of the rectangle in cms is -
- A.
8.5
- B.
9.6
- C.
10.5
- D.
14.4
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Correct answer: D
The area of a square with side s is s² (s × s), and the area of a rectangle with length l and width w is l × w. When two regions have equal area, their area expressions can be set equal to each other and solved for the unknown dimension.
The square has side 6 cm, so its area = 6 × 6 = 36 sq cm.
Let the rectangle's length be L cm. Its area = L × 2.5.
Since the two areas are equal: L × 2.5 = 36.
Solving for L: L = 36 ÷ 2.5 = 14.4.
Check: 14.4 × 2.5 = 36, which matches the square's area (6 × 6 = 36), confirming the length is 14.4 cm.