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The area of a rectangle is 35m^2
, and the length of the rectangle is 3m
more than twice the width. Find the dimensions of the rectangle.

Respuesta :

penfila11Pen
 Hey there :)

Let us change the sentence into mathematics:
Area of rectangle = 35 m²
Length of rectangle is 3 m more than twice the width = 3 + 3w
Width = w

We know the area formula of a rectangle
Area = length × width

Dimensions of the rectangle are:
35 = w ( 3 + 2w )
35 = 3w + 2w²

Take all values to one side and equate to 0

2w² + 3w - 35 = 0

Factor:
( 2w - 7 ) ( w + 5 ) = 0
 w = [tex] \frac{7}{2} = 3.5 m[/tex] or w = - 5 ( Reject because lengths can never be negative )

Therefore the dimensions are:
Width = 3.5 m
Length = 3 + 2 ( 3.5 ) = 10 m

The dimensions of the rectangle are 10m and 3.5m

The formula for the area of a rectangle = length x width

Length = 3m +2w

width = w

area = 35

35 = w x (3 + 2w)

35 = 3w + 2w²

The value of w can be solved using quadratic formula

2w² + 3w - 35 = 0

Multiply 2w² by -35 = -70w²

Determine factors of -70w² that add up to 3w

The factors are 10w -7w

2w² + 10w -7w - 35 = 0

2w(w + 5) -7(w + 5) = 0

2w - 7 = 0

2w = 7

w = 3.5

or

w + 5 = 0

w = -5

3.5 is the value of the width because width cannot be a negative number

Length = (3.5 x 2) + 3 = 10m

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