Question
Download Solution PDFThe length of the rectangle is three times its breadth. If its length is decreased by 7 cm and breadth is increased by 7 cm, its area is increased by 21 cm2. The length of the first rectangle is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
Length (L) = 3 × Breadth (B)
New length = L - 7
New breadth = B + 7
Area increased by 21 cm2.
Concept:
Rectangle area = Length × Breadth.
Calculation:
From the given, we have two equations: L = 3B and (L - 7)(B + 7) - LB = 21.
⇒ Substituting L = 3B into the second equation, we get (3B - 7)(B + 7) - 3B² = 21.
⇒ Solving this quadratic equation, we get B = 5.
⇒ Hence, L = 3 × 5 = 15 cm.
Therefore, the length of the first rectangle is 15 cm.
Last updated on Jul 7, 2025
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