the length of a park is 8 metre more than breadth .if area of park is 240 m sq.then find the length and breadth of park
Answers
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Answer:
The length of the rectangular park is 20 metre.
The breadth of the rectangular park is 12 metre.
Step-by-step-explanation:
Let the length and breadth of the park be l and b respectively.
From the given condition,
Length = Breadth + 8
⇒ l = b + 8 - - ( 1 )
Now, we know that,
Area of rectangle = length × breadth
⇒ 240 = l × b
⇒ 240 = ( b + 8 ) × b - - [ From ( 1 ) ]
⇒ 240 = b² + 8b
⇒ b² + 8b - 240 = 0
⇒ b² + 20b - 12b - 240 = 0
⇒ b ( b + 20 ) - 12 ( b + 20 ) = 0
⇒ ( b + 20 ) ( b - 12 ) = 0
⇒ b + 20 = 0 or b - 12 = 0
⇒ b = - 20 or b = 12
But, the breadth can't be negative.
∴ b = - 20 is not acceptable.
∴ b = 12 metre
Now, by substituting b = 12 in equation ( 1 ), we get,
l = b + 8 - - ( 1 )
⇒ l = 12 + 8
⇒ l = 20 metre
∴ The length of the rectangular park is 20 metre.
The breadth of the rectangular park is 12 metre.