What are these Dimensions?

Question

When Europeans arrived in America, many native Americans of the Northeast lived in longhouses that sheltered several related families. The rectangular floor area of a typical Huron longhouse was about 2750 ft^2. The length was 85 ft greater than the width. What were the dimensions of the floor?

Answer 1

Austin, let's let w = the width of the floor. Then the length is w + 85, right?

 

How do we find the area? length x width.

 

2750 = w(w + 85)

2750 = w² + 85w

     0 = w² + 85w - 2750

     0 = (w + 110)(w - 25)

 

w + 110 = 0

          w = -110. Because length can't be negative, this answer is out.

 

w - 25 = 0

       w = 25

 

So, the width is 25 and the length is 85 more than that, is 110.

 

Hope this helps!