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
