Dimensions of a frame

Question

The area of the rubber coating for a flat roof was 96 ft^2 . The rectangular frame the carpenter built for the flat roof has dimensions such that the length is 4 feet longer than the width. What are the dimensions of the frame?

Answer 1

Area = Length*Width

• Area = 96 ft²
• Length - Width+4

 

Area = Length*Width

96 = (Width+4)*Width

96 = Width² + 4 Width

0 = Width² + 4Width - 96

 

Factors to:

 

0 = (Width-8)(Width+12)

Width = 8 and -12

 

Since you can't have a negative length, Width = 8 feet.  Length = Width + 4 = 8 + 4 = 12 feet