The length of a rectangle is 3 ft longer than its width. If the perimeter of the rectangle is 30 ft , find its area.

Question

I just need to understand how to do this. 

Answer 1

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

 

 

p.s., Your question, "how to do this?" is important; although getting the right answer provides motivation, math is really about learning the best process to use to solve the problem !

Answer 2

Dear Alicia,

 

     Hello, let's look at some steps to follow to solve the problem:

 

  1.  Highlight or underline all the key words or numbers in the story problem.

 

 

  2.  Then translate the words into symbols:

                                                           Let W=width

 

                                      L=     W  +3                                                                             P= 30 ft          A=?

The length of a rectangle is 3 ft. longer than its width.  If the perimeter of the rectangle is 30 ft., find its area.

 

     W= width

 

So L= W + 3     P=30 ft.    

 

3.  Now use the perimeter formula to find the width of the rectangle, so that later, you can find its area.

 

P= 2(L) + 2 (W)                                  30 = 2(L)+ 2(W)     

            

 

4.  Substitute the values into the perimeter equation:    30 = 2(W+3) + 2(W)

 

                                                                                 30= 2W +6 +2W= 4W +6

 

 

5.  Solve for "W."   Take 6 from both sides:          24=  4W      

                         

 

6.  Divide both sides of the equal sign by the number next to "W."        24/4   =W       6=Width

 

 

7. Since the width is 6, the length is (W +3)= (6+3)=9   

 

 

8.  Area of a rectangle=  A= L* W        

 

9.  Substitute values into Length and width in formula.   A= 9 * 6=54 ft.²      Answer                                                        

Answer 3

Okay, so to start this problem let's figure out what we need.  We need the area, so in order to get the area we need to find out the length and width of the rectangle.  So now let's set up an equation that will help us figure those out.  Pulling the pieces of information from the question that we need we can set this up:

 

The perimeter of a rectangle can be described as 2x + 2y (where x and y are the length and width).

 

But the question gives us a huge hint that the length is 3 feet longer than the width.

 

If we make the width x, we can replace the y from the above equation with x + 3:

 

2x + 2(x+3) = 30.  Now we can do algebra on it and solve for x (the width).

 

Simplify:

 

2x + 2x + 6 = 30

 

Simplify:

 

4x + 6 = 30

 

Subtract 6 from both sides:

 

4x = 24

 

Divide by 4 on both sides:

 

x = 6

 

So this tells us that the width is equal to 6 feet.  Using the given information that the length is 3 feet longer than the width, we now know that the length is 9 feet.

 

So, the area is 6 feet * 9 feet = 54 square feet

 

Check your answer to make sure the perimeter equals 30:

 

(2*6) + (2*9) or 12 + 18 does in fact equal 30.

 

Hope this helps!

 

If you have any more questions just comment on here.