- #1
Albert1
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P is an inner point of equilateral triangle ABC ,
given PC=3, PA=4,PB=5 ,please find the side length of the equilateral triangle
given PC=3, PA=4,PB=5 ,please find the side length of the equilateral triangle
Please find the side length of an equilateral triangle
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- Thread starter Albert1
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In summary, an equilateral triangle is a type of triangle with three equal sides and angles of 60 degrees. To find the side length, you can use the formula s = P/3, where s is the side length and P is the perimeter. The Pythagorean theorem cannot be used for equilateral triangles. All equilateral triangles are the same size, but can have different orientations. To prove that a triangle is equilateral, you need to show equal side lengths and angles, which can be done through measurement or geometric proofs.
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caffeinemachine
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Rotate the trianlge by 60 degrees about the point C. Let $P'$ be the new position of $P$. Then $\angle P'PA=90$. Thus we get a triangle $CPA$ with $\angle CPA=150$ and $PC=3, PA=4$. To find $AC$.Albert said:
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Albert1
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caffeinemachine
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Brilliant solution!Albert said:
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CellCoree
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.
To find the side length of an equilateral triangle, we can use the fact that all sides of an equilateral triangle are equal. Since we know that PC=3, PA=4, and PB=5, we can set up the following equations:
PC=PA=PB=x (where x represents the side length)
By setting these equations equal to each other, we can solve for x:
3=x, 4=x, 5=x
Therefore, the side length of the equilateral triangle is 3, 4, and 5 units long. It is important to note that this is only one possible solution, as there are multiple equilateral triangles that can have different side lengths but still satisfy the given conditions.
To find the side length of an equilateral triangle, we can use the fact that all sides of an equilateral triangle are equal. Since we know that PC=3, PA=4, and PB=5, we can set up the following equations:
PC=PA=PB=x (where x represents the side length)
By setting these equations equal to each other, we can solve for x:
3=x, 4=x, 5=x
Therefore, the side length of the equilateral triangle is 3, 4, and 5 units long. It is important to note that this is only one possible solution, as there are multiple equilateral triangles that can have different side lengths but still satisfy the given conditions.
Related to Please find the side length of an equilateral triangle
1. What is an equilateral triangle?
An equilateral triangle is a type of triangle where all three sides are equal in length and all three angles are equal at 60 degrees.
2. How do you find the side length of an equilateral triangle?
To find the side length of an equilateral triangle, you can use the formula s = P/3, where s is the side length and P is the perimeter of the triangle. This means that you divide the perimeter by 3 to get the length of each side.
3. Can you use the Pythagorean theorem to find the side length of an equilateral triangle?
No, the Pythagorean theorem only applies to right triangles, where one angle is 90 degrees. Since all angles in an equilateral triangle are 60 degrees, the Pythagorean theorem cannot be used to find the side length.
4. Are all equilateral triangles the same size?
Yes, all equilateral triangles are the same size because they have equal side lengths and angles. The only difference between equilateral triangles is their orientation or position.
5. How can you prove that a triangle is equilateral?
To prove that a triangle is equilateral, you can show that all three sides are equal in length and all three angles are equal at 60 degrees. This can be done by measuring the sides and angles or using geometric proofs.
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