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Question
The perimeter of a rectangle is 82m and its area is `400m^2` . The breadth of the rectangle is
(a) 25m (b)20m
(c) 16m (d)9m
Solution
(c) 16 m
Let the length and breadth of the rectangle be l and b.
Perimeter of the rectangle 82m
⇒`2xx(l+b)=82`
⇒ `l+b=41`
⇒`l=(41-b)` ................(1)
Area of the rectangle =`400m^2`
⇒`lxxb=400m^2`
⇒`(41-b)b=400 ` (using 1)
⇒`41b-b^2=400`
⇒`b^2-41b+400=0`
⇒`b^2-25b-16b+400=0`
⇒`b(b-25)-16(b-25)=0`
⇒`(b-25) (b-16)=0`
⇒`b=25 or b=16`
`If b=25 or b=16`
`l=41-25=16`
Since, l cannot be less than b,
∴`b=16m`
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