Find the length and width of the window (multiple steps)

Question

The length of a rectangular window is 5 feet more than its width, w. The area of the window is 36 square feet. We wish to find both the length and width of the window. Please do the following:

1) Write an equation could be used to find the dimensions of the window USING ONLY ONE VARIABLE (w).
2) Put that equation in standard form (so that all terms are on one side of the equation together equal to zero).
3) FACTOR the quadratic into two binomials.
4) Use the zero product property to solve the equation.
5) Evaluate whether both answers make sense in the context of the question.
6) Write a sentence for your final answer (Ex. The length of the window is ___ ft and the width of the window is ___ ft)

Answer 1

Area = length x width

 

36 = (w + 5) * w     <--- part 1

 

36 = w^2 + 5w

 

0 = w^2 + 5w -  36   <--- part2

 

0 =  ( w    +     9 )(w     -        4   ) <--  part 3

 

 

Parts 4-5:

w + 9 = 0   -->  w = -9     No Good!!! width cannot be negatice

 

w - 4 = 0 --> w-4

 

Width = 4

Length = w + 5 = 9

Area = 4 x 9 = 36

 

The length of the window is 9 ft and the width of the window is 4 feet.