If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, what type of triangle is it?

If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, what type of triangle is it?

• A. Equilateral triangle
• B. Scalene triangle
• C. Obtuse triangle
• D. Right triangle

Answer: (D)

To determine the type of triangle formed by sides of lengths 3 cm, 4 cm, and 5 cm, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. Here, the longest side is 5 cm. We can check if the triangle is a right triangle by calculating: 1. The square of the longest side: \( (5 \, \text{cm})^2 = 25 \) 2. The sum of the squares of the other two sides: \( (3 \, \text{cm})^2 + (4 \, \text{cm})^2 = 9 + 16 = 25 \) Since both calculations yield the same result (25), this confirms that the triangle is indeed a right triangle. Thus, the correct classification for this triangle is that it is a right triangle. The other classifications do not fit this triangle. An equilateral triangle would have all sides of equal length, a scalene triangle would have all sides of different lengths, and an obtuse triangle

To determine the type of triangle formed by sides of lengths 3 cm, 4 cm, and 5 cm, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Here, the longest side is 5 cm. We can check if the triangle is a right triangle by calculating:

1. The square of the longest side:

( (5 , \text{cm})^2 = 25 )

2. The sum of the squares of the other two sides:

( (3 , \text{cm})^2 + (4 , \text{cm})^2 = 9 + 16 = 25 )

Since both calculations yield the same result (25), this confirms that the triangle is indeed a right triangle. Thus, the correct classification for this triangle is that it is a right triangle.

The other classifications do not fit this triangle. An equilateral triangle would have all sides of equal length, a scalene triangle would have all sides of different lengths, and an obtuse triangle