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