Answer: The backyard is 30 meters by 40 meters
30 meters = horizontal dimension
40 meters = vertical dimension
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Explanation:
The pool on paper is 7.5 units across horizontally. Applying the scale factor, we can see that it corresponds to 7.5*2 = 15 meters
The 20 meter portion is vertical. On paper, we see that it's 10 units tall. So the "times 2" operation applies to jump from 10 cm to 20 meters
Or you could note that the ratio 1 cm : 2 m scales up to 10 cm : 20 m after multiplying both parts by 10.
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With that in mind, all we need to do really is count the number of squares across the top and along the left side. Across the top, we have 15 squares. That 15 cm corresponds to 15*2 = 30 meters in length.
Along the left side, the figure is 20 cm tall. So that corresponds to 20*2 = 40 meters.
The backyard is 30 meters by 40 meters. This includes the backyard, shed, and other features in the diagram. The entire backyard is 30*20 = 600 square meters. If you wanted to know the area of the grass only, then you'd subtract off the areas of the pool, shed, etc.
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Your teacher mentions that the pool is similar to the backyard overall. Since we're in a geometry setting, the word "similar" is very specific of course.
We can match up the corresponding lengths to form a proportion like so
(large horizontal)/(small horizontal) = (large vertical)/(small vertical)
30/15 = 40/20
2 = 2
So that confirms we have similar figures, at least in terms of the sides being proportional. Everything being a rectangle helps show that all angles are the same.
