Question
Download Solution PDFThe area of a rectangle increases by 8 m2 if its length is increased by 5 m and breadth is decreased by 7 m. If the length is decreased by 5 m and breadth is increased by 8 m, then its area increases by 33 m2. What is the perimeter of the original rectangle (in m)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Scenario 1: Length increased by 5 m, Breadth decreased by 7 m, Area increases by 8 m2.
Scenario 2: Length decreased by 5 m, Breadth increased by 8 m, Area increases by 33 m2.
Formula used:
Area of rectangle = Length × Breadth (l × b)
Perimeter of rectangle = 2 × (Length + Breadth)
Calculations:
Let the original length of the rectangle be 'l' meters and the original breadth be 'b' meters.
Original Area = l × b
From Scenario 1:
New length = (l + 5) m
New breadth = (b - 7) m
New Area = (l + 5)(b - 7)
Given that the area increases by 8 m2:
(l + 5)(b - 7) = lb + 8
⇒ lb - 7l + 5b - 35 = lb + 8
⇒ -7l + 5b = 8 + 35
⇒ -7l + 5b = 43 (Equation 1)
From Scenario 2:
New length = (l - 5) m
New breadth = (b + 8) m
New Area = (l - 5)(b + 8)
Given that the area increases by 33 m2:
(l - 5)(b + 8) = lb + 33
⇒ lb + 8l - 5b - 40 = lb + 33
⇒ 8l - 5b = 33 + 40
⇒ 8l - 5b = 73 (Equation 2)
Now, we have a system of two linear equations:
1) -7l + 5b = 43
2) 8l - 5b = 73
Add Equation 1 and Equation 2:
(-7l + 5b) + (8l - 5b) = 43 + 73
⇒ -7l + 8l + 5b - 5b = 116
⇒ l = 116
Substitute the value of l into Equation 1:
-7(116) + 5b = 43
⇒ -812 + 5b = 43
⇒ 5b = 43 + 812
⇒ 5b = 855
⇒ b = 171
So, the original length (l) = 116 m and original breadth (b) = 171 m.
Perimeter of the original rectangle = 2 × (l + b)
⇒ Perimeter = 2 × (116 + 171)
⇒ Perimeter = 2 × 287
⇒ Perimeter = 574 m
∴ The perimeter of the original rectangle is 574 m.
Last updated on Jul 17, 2025
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