The area of a rectangle is 63 square feet, and its perimeter is 33 feet. What are the dimensions of the rectangle?

Question

The area of a rectangle is 63 square feet, and its perimeter is 33 feet. What are the dimensions of the rectangle?

Systems of equations or inequalities

 

Answer 1

W - width of the recangle

 

L - length of a rectangle

 

 P - Perimeter of Rectangle

 

  A - area of a rectangle:

 

   P = 2W + 2L = 33 ft    (1)

    A = wL  = 63 ft^2       (2)

 

   W = (33 - 2 L ) / 2      / from (1)

 

    L ( 33 - 2L ) /2 = 63      / Substitute into ( 2)

 

     33 L - 2 L^2  = 126

 

      2L^2 - 33L + 126 =0

 

     2L^2 -12 L - 21L + 126 =0

 

       2L ( L - 6 ) - 21 ( L - 6 ) =0

 

        (2L - 21 ) ( L- 6 ) =0

 

       2L - 21 = 0      L = 21/2 ft

 

         L - 6 = 0       L = 6 = W 

 

      (  W, L ) = ( 6, 21/2 Ft)