Twelve equal squares are placed to fit in a rectangle of diagonal 5 cm. There are three rows containing four squares each. No gaps are left between adjacent squares. What is the area of each square?
Correct Answer: Option C
Explanation
1. First, I visualize the arrangement. The question says there are '3 rows containing 4 squares each'. If I assume the side of one small square is 's', then the total height of the rectangle is 3s and the length is 4s.\n2. Now I look at the diagonal. A rectangle with sides 3s and 4s forms a right-angled triangle. \n3. From my analysis of PYQs (like the 2014 and 2016 direction questions), I know the 'Pythagorean Triplet' (3, 4, 5) is a standard pattern [46]. This means if the legs are 3 and 4, the diagonal must be 5. \n4. So, in terms of 's', the diagonal is 5s.\n5. The question gives the actual diagonal as 5 cm.\n6. I use the Unitary Method (Scaling) [51]: If 5s = 5 cm, then s = 1 cm.\n7. The question asks for the area of one square. Area = side × side = 1 × 1 = 1 sq cm.\n8. This matches option (C). No complex calculation was needed, just matching the 3-4-5 pattern to the given data.
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