Question

A plot of land doubles in size by adding x meters to the length and x meters to the width of the land?if the original plot had an area of 200 by 300 meters ,what is the value x?

Answer 1

Answer:

  x = 100

Step-by-step explanation:

The larger area is ...

  A = LW

  A = (300+x)(200+x) = x^2 +500x +60,000

The smaller area is ...

  A = (200)(300) = 60,000

We want the larger area to be double the smaller area, so ...

  x^2 +500x +60,000 = 2(60,000)

  x^2 +500x = 60,000 . . . . . . . . . . . . subtract 60,000

  x^2 +500x + 62500 = 122500 . . . add 250^2 to complete the square

  (x +250)^2 = 350^2

We're interested in the positive solution, so we can take the positive square root to find it:

  x +250 = 350

  x = 100 . . . . . . . . . subtract 250

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The graph shows the quadratic in the form x^2 +500x -60,000. That is, we're looking for zeros (x-intercepts) of the function.