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igomit [66]
2 years ago
9

Arrange the integers 1,4,8,12,17,32 so that all consecutive integers add to a perfect square. Enter your answer with numbers sep

arated by commas.​
Mathematics
1 answer:
viktelen [127]2 years ago
6 0

One possible answer is: 1, 8, 17, 32, 4, 12

I don't know if there's a methodical way to get this answer. I used trial and error. I started with 1 and looked through the list to see what adds to 1 to get a perfect square. That would be 8 since 1+8 = 9 = 3^2

The process is repeated but this time for 8. After a bit of guess and checking, we see that 8+17 = 25 = 5^2.

Then after 17 is 32 because 17+32 = 49 = 7^2.

Keep doing this until all of the values are used up. If you get stuck, then try backtracking to a previous branch/path where everything worked and try another fork in the road. If that doesn't work, then try starting the sequence with a completely different value (instead of 1).

Other answers may be possible. I haven't checked all possible permutations.

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Answer:

4.5

Step-by-step explanation:

∠BAC ~ ∠EDF means that the triangles are similar. So the legs of the triangle share the same proportions, even if the sizes are different.

Since they share the same proportions, the same operations can be performed on each base to find the area.

The answer can be found with the knowledge that the area of a triangle is half of the height * width. You know the width of ∠BAC is 4, and the area is 8, so 16 (the area doubled) / 4 is the height. The width and height of ∠BAC are the same, and since the proportions are also the same, the width and height of ∠EDF are both 3. So the area is the width (3) times the height (3) divided by 2.

3*3 = 9

9/2 = 4.5

So the area is 4.5

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