Question 674411
draw and label a rectangle that has a perimeter of 60 cm and an area of 200 square centimeters
<pre>
       Perimeter = 2×Length + 2×Width
            Area = Length×Width

              60 = 2L + 2W
             200 = LW

Splve the first equation for W and substitute in the second equation:

              60 = 2L + 2W

Divide through by 2

              30 =  L +  W

          30 - L = w 


Substitute (30 - L) for W in

             200 = LW

             200 = L(30 - L)

             200 = 30L - L²

Get 0 on the right:

  L² - 30L + 200 = 0

Factor the left side:

(L - 20)(L - 10) = 0

Use the zero-factor property:

  L - 20 = 0;   L - 10 = 0
       L = 20;       L = 10

Subdtitute in

  30 - L = w    30 - L = w    
 30 - 20 = W   30 - 10 = W 
      10 = W        20 = W

We usually think of the length as the longer side, so

the length is 20 and the width is 10


{{{drawing(711,355.5,0,20,0,10,
line(0,0,20,0),
line(0,1,20,1),
line(0,2,20,2),
line(0,3,20,3),
line(0,4,20,4),
line(0,5,20,5),
line(0,6,20,6),
line(0,7,20,7),
line(0,8,20,8),
line(0,9,20,9),
line(0,10,20,10),
line(0,0,0,10),
line(1,0,1,10),
line(2,0,2,10),
line(3,0,3,10),
line(4,0,4,10),
line(5,0,5,10),
line(6,0,6,10),
line(7,0,7,10),
line(8,0,8,10),
line(9,0,9,10),
line(10,0,10,10),
line(11,0,11,10),
line(12,0,12,10),
line(13,0,13,10),
line(14,0,14,10),
line(15,0,15,10),
line(16,0,16,10),
line(17,0,17,10),
line(18,0,18,10),
line(19,0,19,10),
line(20,0,20,10)


 )}}}Width = 10 centimeters
                  Length = 20 centimeters

Edwin</pre>