Question

15pts and brainliest to whoever can answer

Answer 1

9514 1404 393

Answer:

  p = 3x+10

Step-by-step explanation:

The attached diagram pretty much explains it.

The unknown dimension at the top was the subject of a previous problem. It is the difference in length between the two marked horizontal segments:

  (2x +15) -(x) = x +15 . . . . . length of unmarked solid horizontal line

Similarly, the length of the unmarked vertical line on the right is the difference between the marked vertical lines:

  (2x -5) -(x -5) = x . . . . . length of unmarked solid vertical line

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The formula for the area of a rectangle is used to find the areas of the left-side and right-side rectangles. Respectively, those areas are ...

  left-side area = x(2x -5)

  right-side area = x(x +15)

Then the total area enclosed by the solid line is ...

  x(2x -5) +x(x +15) = x(2x -5 +x +15) = x(3x +10)

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The area of the lot extension is the product of its dimensions:

  extension area = x·p

We want this to be the same as the area in the solid line, so ...

  x·p = x·(3x +10)

Dividing by the coefficient of p (which is x), we have ...

  p = 3x +10