What is the perimeter of the rectangle in units?

Question

The area of a rectangle is 2x²-11x-63 square units and the length is 2x+7. What is the perimeter, in units, of the rectangle?

Answer 1

Area/length = width

 

So the width is

 

(2x^2 - 11x - 63)/(2x+7) =

 

( 2x     +      7)(x    -     9  )/(2x+7)  <--- factors

 

= x - 9     provided x is not -7/2

 

The perimeter is 2L + 2W = 2(x-9) + 2(2x+7)

                                       = 2x - 18 + 4x + 14

                                        = 6x - 4

                                         = 2(3x - 2)

 

 

Check :

  Let x = 10

 

  The area is 2(10)^2 -11(10) - 63 =

                  2(100) - 11(10) - 63 =

                  200 - 110 - 63 = 

                90 - 63 =

              27

 

The length is 2(10) + 7 = 20 + 7  = 27

The width is 10 - 9 = 1

 

The area is in fact 1*27= 27.

The perimeter is 2(27) + 2(1) = 54 + 2 = 56

and 2 ( 3*10 - 2) = 2(30 -2) = 2(28) = 56