Question
Download Solution PDFThe ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Ratio of perimeter to breadth = 5 : 1
Area of rectangle = 216 sq. cm
Formula used:
Perimeter of rectangle = 2 × (length + breadth)
Area of rectangle = length × breadth
Calculations:
Let the breadth be 'b' cm.
Then, the perimeter = 5b cm.
Perimeter = 2 × (length + breadth)
⇒ 5b = 2 × (length + b)
⇒ 5b = 2 × length + 2b
⇒ 3b = 2 × length
⇒ length = 1.5b
Area = length × breadth
⇒ 216 = 1.5b × b
⇒ b2 = 216 / 1.5
⇒ b2 = 144
⇒ b = 12 cm
length = 1.5 × 12 = 18 cm
∴ The length of the rectangle is 18 cm.
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