MATH SOLVE

3 months ago

Q:
# 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.

Accepted Solution

A:

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

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