Question

The length of a rectangle exceeds twice its width by 1 metre. If the area of the rectangle is 55 sq. m, find its length and width.

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Answer 1

HEYA!!!

Given,

area of rectangle = 55sq.m

let the breadth of rectangle = x

length of the rectangle = 2x + 1

Area of rectangle = l × b

= x ( 2x + 1 )

= 2x^2 +1

55-1 = 2x^2

54. = $2 {x}^{2}$

54/2 = x^2

27. = x^2

x = $\sqrt{27}$

Therefore breadth of rectangle = 5.19cm

then it's length =( 5.19× 2) +1

= 10.38 + 1

= 11.38..

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Answer 2

let the width of rectangle be ' L '

then, its length will be (2L + 1)

area of rectangle = length x width

L x (2L + 1) = 55

2L^2 + L = 55

2L^2 + L - 55 = 0

2L^2 - 10L + 11L - 55 = 0

2L ( L - 5) + 11 ( L - 5) = 0

( 2L + 11) ( L - 5 ) = 0

2L + 11 = 0. OR. L - 5 = 0

L = - 11/2. OR. L = 5

since length can't be negative so
L cannot be equal to - 11/2
so L = 5

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