The city planning committee wants one tree planted every 20 ft along Dayton Ave. if the perimeter of the plot of land is 234 ft
about how many trees will be planted. explain. 12 is an incorrect answer.
2 answers:
Answer:
2 trees
Step-by-step explanation:
Since the city is planting a tree every 20 feet across Dayton Avenue, then we need to find the length of the side that is on Dayton Avenue.
We are missing 3 sides to this. But it's extremely important to note that the side adjacent to Dayton Avenue is the same length as the other missing two sides combined. This is because both of these lengths contain the 1 feather and 2 feather mark - these signify congruence.
This means that the side lengths of both of them combined will be
This means the side adjacent to Dayton Avenue is
feet long.
Now that we know that the side is 57 feet long, we have to divide this by 20, as a tree is being placed every 20 feet. If we get a decimal, we will have to round down because it gets planted only, and only if, 20 more feet has been accomplished. If we are a fraction of the way there, a tree doesn't get planted.
Rounding down gets us 2.
Hope this helped!
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Consider two triangles AEB and CEF. In these triangles:
- ∠AEB≅∠CEF (as vertical angles);
- ∠EAB≅∠ECF (lines AB and CD are parallel and AC is transversal, then these angles are congruent as alternate interior angles);
- ∠ABE≅∠CFE (lines AB and CD are parallel, BF is transversal, then these angles congruent as alternate interior angles).
Thus, by AAA theorem,
Corresponding sides of similar triangles are proportional, then
ABCD is a parallelogram, then AB=CD.
Therefore,
CD=2CF and CD=DF+CF. Equate these two expressions:
DF+CF=2CF,
DF=CF.
This gives you that DF:CF=1:1.
Answer: 1:1