Requtangle shed has the area of 77sq.ft. The length is 3eet less than twice the width. Find L & W.

Question

The floor of a shed has an area of 77sq.ft. the floor is a rectangle space length is 3feet less than twice the width. Find L & W.   This is in the factorization chapter.

Answer 1

Let w= width    and l= 2w-3

 

Equation for the situation:  w(2w-3) = 77

 

Go ahead and distribute the w, and move the 77 to the same side.

 

Equation: 2w² -3w - 77 =0

 

Now you can either factor it by the AC method or use the quadratic formula to solve for x.

 

2*77= 154, now we list factors of 154 and choose the pair to subtract to be -3.

 

154

1 *154

2 *77

7 *22

11 *14   11-14= -3

                              2w² -14w + 11w -77 = 0   Now group the first 2 terms and last two terms.  

  

                              (2w² -14w) + (11w - 77)  = 0   Now factor out what is common in the first group and 2nd group.

 

                             2w (w - 7) + 11 (w - 7)  = 0  Now factor out the common binomial in 1st parenthesis and left over

 

                             (w - 7) (2w + 11) = 0          Now set each of them equal to zero.

 

                             w - 7 = 0        2w + 11 = 0     Now solve for w, remember look for the positive value since

                                                                         dealing in measurements.

                           w = 7 ft     or    w =  -11/2 ft

 

Thus we choose W = 7ft, then plug it back in to get what L will equal.   L = 2 (7) -3,  L = 11ft.

 

W= 7ft

L = 11ft