The length of your room is 2 ft more than three times the width. If the area is 16 ft, find the width and the length.

Question

I need help.

Answer 1

Let width = x

Let length = 3x+2

 

Area = length * width = 16

 

x(3x + 2) = 16

 

3x^2 + 2x = 16

 

3x^2 + 2x - 16 = 0

 

(3x + 8)(x - 2) = 0 

 

For distance, we don't use negative answers. So we will only set the second factor equal to zero.

 

x - 2 = 0

 

x = 2

 

The width is 2 feet. The length is 3(2) + 2 which equals 8 feet. 

 

Side note: Area is always measured in square units. So the area of the room should read as 16 square feet instead of 16 feet.

 

 

Answer 2

w=width

3w+2=length

A=l*w

16=(3w+2)*w

16=3w²+2w

3w²+2w-16=0

(3w+8)(w-2)=0

don't use 3w+8 because it gives you a negative number

w-2=0

w=2

l=3(2)+2

l=6+2

l=8 ft and w=2 ft