The sum of the length and breadth of a rectangle is 6 cm. A square is constructed such that one of its sides is equal to a diagonal of the rectangle. If the ratio of areas of the square and rectangle is 5 : 2, the area of the square in cm2 is?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 20
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Understanding |
Application |
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Let the length of the rectangle be x cm and breadth of rectangle = (6 – x) Side of the square = diagonal of the rectangle = a cm So, Area of square = a2 And Area of rectangle = x × (6 – x)
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According to the question: a2 = x2 + (6 – x)2 ⇒ a2 = x2 + 36 + x2 – 12x ⇒ a2 = 2x2 – 12x + 36 According to the question: (2x2 – 12x + 36)/(6x – x2) = 5/2 ⇒ 4x2 – 24x + 72 = 30x – 5x2 ⇒ 9x2 – 54x + 72 = 0 ⇒ x2 – 6x + 8 = 0 ⇒ x2 – 4x – 2x + 8 = 0 ⇒ x (x – 4) – 2 (x – 4) = 0 ⇒ (x – 4) (x – 2) = 0 ⇒ x = 4 and x = 2 Hence, Area of square = a2 = x2 + (6 – x)2 = 22 + 42 = 20 cm2 |