Find the length and width of the rectangle

Question

A rectangle with perimeter 26cm has an area of 40cm^2. Find the length and width of the rectangle?

Answer 1

Find the factor pairs of the area 40:

 

1 x 40; 2 x 20; 4 x 10; 5 x 8

 

Half of the perimeter 26 is 13, so your dimensions must be a factor pair that adds up to 13

 

8 x 5 is 40, 8 PLUS 5 is 13.

 

Your dimensions are 8 by 5.

Answer 2

A rectangle with perimeter 26cm has an area of 40cm^2. Find the length and width of the rectangle?

 

Let:

  L = length of rectangle

  W = width of rectangle

 

The formulas are:

   Perimeter = 2L + 2W      (or L+W+L+W, the distance around)

   Area = LW

 

P = 26 = 2L + 2W

        L + W = 13               (rewrite; divide everything by 2)

A = 40 = LW

        L = 40/W

 

Now, substitute the value for L (second equation) into the first equation:

        40/W + W = 13

         40 + W^2 = 13W             (multiply everything by W)

         W^2 -13 + 40 = 0           (rearrange)

Now, either factor or use quadratic equation.

         (W-5)(W-8) = 0

        Either W=5 and L=8           (putting value for W into W+L = 13)

             or  W=8 and L=5