Question
Download Solution PDFThree times the length of a rectangle is equal to seven times its breadth. The area of the rectangle is 2352 sq. cm. What is the area of a square whose perimeter is equal to that of the rectangle?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF3 × Length = 7 × Breadth ⇒ Length : Breadth = 7 : 3 ⇒ Let Breadth = 3k, Length = 7k
Area of Rectangle = Length × Breadth = (7k) × (3k) = 21k² = 2352
⇒ k² = 2352 ÷ 21 = 112 ⇒ k = √112 = 4√7
⇒ Breadth = 3k = 3 × 4√7 = 12√7
⇒ Length = 7k = 7 × 4√7 = 28√7
Perimeter of Rectangle = 2(L + B) = 2(28√7 + 12√7) = 2 × 40√7 = 80√7
Square with same perimeter:
Let side of square = s ⇒ 4s = 80√7 ⇒ s = 20√7
Area of square = s² = (20√7)² = 400 × 7 = 2800 sq cm
Thus, the correct answer is 2800 sq cm.
Last updated on Jul 8, 2025
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