1.

The perimeter of a rectangle is 82m and its area is `400m^2`. The breadth of the rectangle is: (a)25 m (b) 16 m (c)9 m (d)20 m

Answer» Let length of rectangle is `l` and breadth is `b` in metres.
Perimeter of a rectangle `(P) = 2(l+b)`
`:. 2(l+b) =82`
`=>l+b = 41=>l=41-b->(1)`
Area of a rectangle `(A) = l**b `
`=>l**b = 400`
From (1),
`=>(41-b)b = 400`
`=>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 = 16 and b = 25`
When `b = 16m, l = 41-16 = 25m`
When `b = 25m, l = 41-25 = 16m`


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