Question

Please help The perimeter of a rectangular shape electronic keyboard is 14 ft. Its width is 3 ft longer than its depth

Answer 1

Answer:

Width = 6ft Area = 54 sq ft

Step-by-step explanation:

First, re-read the problem until you understand it and can put it into your own words.  I re-wrote it like this:  "Find the area of a rectangle by first finding the length (L) and the width (W)."   [note that I added "find L and W," but that is how I'm going to solve the problem;  I could also have said that we will need the formulas, P=2L+2W and A=LW, but you knew that already, right?).

 

Translate the problem:

 "The length of a rectangle is 3 ft longer than its width"      means

         L                             =    3             +         W                 (eq1)

 "the perimeter of the rectangle is 30 ft"     means

            P                                = 30                      (eq2)

 

So, now the math is easy, just find L and W so we can compute the area:

     P = 30 = 2L + 2W                         (eq3; from eq2 and the formula for P)

          30 = 2(3+W)  +  2W              (use eq1 to substitute for L)

          30 = 6 + 2W   + 2W              (distribute)

           30 = 6 + 4W                       (collect terms)

            24 = 4W                        (subtract 6 from both sides)

            6 ft = W                         (divide both sides by 4)

 

Use the easiest equation (either eq1 or else eq3) to find L:

          L = 3 + W        (eq1)

          L = 3 + 6

          L = 9 ft

What is the area (A)?

          A = L*W

          A = (9 ft)*(6 ft)

          A = 54 sq ft