WORD PROBLEM (AREA OF RECTANGLE)

Question

The width of a rectangle is 8 inches less than the length. The area is 48 square inches. Find the length and width. Round to the nearest tenth if necessary.

 

PLEASE SHOW WORK AND RIGHT THE FINAL ANSWERS IN BOLD PRINT

Answer 1

The Area of a rectangle is Length*Width.   Let's use L and W.

 

"width of a rectangle is 8 inches less than the length"   means

    W                        =       -8                    +  L     [eq1]

 

"area is 48 square inches"    means    L*W = 48       [eq2]

 

Substitution method:

   Solve for one variable in eq1 and put that into eq2.

      W = L - 8

 

      L*(L-8) = 48

     L² - 8L - 48 = 0             [subtract 48 from both sides]

     (L-12)(L+4) = 0             [either factor or use quadratic formula;  check using F-O-I-L)

  Either L=12 or L=-4 or both       [Multiplicative Property of Zero]

    Note: Length of -4 does not make sense; ignore it.

     L = 12

Put that into either equation to determine W (note: eq1 is easiest]

    W = 12 - 8 = 4

 

Checking (very important):

   Is  4 = 12 - 8   ?

        4 = 4   ?yes

   Is  12*4 = 48   ?

         48 = 48   ?yes