Question

Anyone? Know how to do this?

Answer 1

Answer:

• x = 4
• length = 19 ft
• width = 11 ft

Step-by-step explanation:

The area is given by the product of length and width.

  A = LW

  209 = (4x +3)(4x -5)

  209 = 16x^2 -8x -15

  224 = 16x^2 -8x

You could rearrange and use the quadratic formula at this point, but we elect to "complete the square".

  14 = x^2 -(1/2)x

  14 +1/16 = x^2 -1/2x +(1/4)^2 . . . . . add the square of half the x-coefficient

  (x -0.25)^2 = 14.0625

  x = 0.25 ± 3.75 . . . . . . take the square root; add 0.25

Only positive values of x are useful here, so we have

  x = 4

Then the dimensions are ...

  length = 4x +3 = 4(4) +3 = 19 . . . feet

  width = 4x -5 = 16 -5 = 11 . . . feet