Question
Download Solution PDFThe length and breadth of a rectangle are in the ratio 3 : 2. If the length is increased by 5 m keeping the breadth same, the new area of rectangle is 2600 m2. What is the perimeter of the original rectangle?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Length : breadth = 3 : 2
Length is increased by 5 m keeping the breadth same
New area become 2600 m2
Formula used:
Area of rectangle = Length × breadth
Perimeter = 2 (Length + breadth)
Calculation:
Let length & breadth be '3y' & '2y' respectively.
According to the question
⇒ (3y + 5) × 2y = 2600
⇒ 6y2 + 10y = 2600
⇒ 6y2 + 10y - 2600 = 0
⇒ 3y2 + 5y - 1300 = 0
⇒ 3y2 - 60y + 65y - 1300 = 0
⇒ 3y(y - 20) + 65(y - 20) = 0
⇒ (3y + 65)(y - 20) = 0
⇒ y = 20, y ≠ - (65/3)
Since, length can not be negative.
Therefore, length & breadth of original rectangle
3y = 3 × 20 = 60
2y = 2 × 20 = 40
Hence, perimeter = 2(60 + 40) = 200
∴ Perimeter of the rectangle is 200 m.
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