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If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, what type of triangle is it?
- a)Equilateral
- b)Isosceles
- c)Scalene
- d)Right-angled
Correct answer is option 'D'. Can you explain this answer?
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If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, what type of ...
Understanding the Triangle
A triangle with sides of lengths 3 cm, 4 cm, and 5 cm is an interesting case. Let's analyze its properties:
Types of Triangles
- Equilateral Triangle: All three sides are equal in length. In this case, 3 cm, 4 cm, and 5 cm are not equal.
- Isosceles Triangle: Two sides are equal in length. Again, in this case, none of the sides are the same.
- Scalene Triangle: All three sides are of different lengths. While this triangle is scalene, it also has another important property.
Checking for Right-Angled Triangle
To determine if a triangle is right-angled, we use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (longest side) equals the sum of the squares of the lengths of the other two sides.
- Sides: 3 cm, 4 cm (the two shorter sides), and 5 cm (the longest side).
- Applying the theorem:
- 5^2 = 3^2 + 4^2
- 25 = 9 + 16
- 25 = 25
Since the equation holds true, the triangle with sides 3 cm, 4 cm, and 5 cm is confirmed to be a right-angled triangle.
Conclusion
Thus, the correct answer is option 'D', indicating that the triangle is a right-angled triangle. This is a classic example often used to illustrate the properties of triangles!
A triangle with sides of lengths 3 cm, 4 cm, and 5 cm is an interesting case. Let's analyze its properties:
Types of Triangles
- Equilateral Triangle: All three sides are equal in length. In this case, 3 cm, 4 cm, and 5 cm are not equal.
- Isosceles Triangle: Two sides are equal in length. Again, in this case, none of the sides are the same.
- Scalene Triangle: All three sides are of different lengths. While this triangle is scalene, it also has another important property.
Checking for Right-Angled Triangle
To determine if a triangle is right-angled, we use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (longest side) equals the sum of the squares of the lengths of the other two sides.
- Sides: 3 cm, 4 cm (the two shorter sides), and 5 cm (the longest side).
- Applying the theorem:
- 5^2 = 3^2 + 4^2
- 25 = 9 + 16
- 25 = 25
Since the equation holds true, the triangle with sides 3 cm, 4 cm, and 5 cm is confirmed to be a right-angled triangle.
Conclusion
Thus, the correct answer is option 'D', indicating that the triangle is a right-angled triangle. This is a classic example often used to illustrate the properties of triangles!
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Community Answer
If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, what type of ...
This is a right-angled triangle because the lengths satisfy the Pythagorean Theorem (32 + 42 = 52). It's a 3-4-5 right triangle.
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If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, what type of triangle is it?a)Equilateralb)Isoscelesc)Scalened)Right-angledCorrect answer is option 'D'. Can you explain this answer?
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