Which?
Of the following can be side of a right angled triangle= 2.4cm,3.2cm,4.0cm

To determine if these lengths can be the sides of a right-angled triangle, we need to check if they satisfy the Pythagorean theorem. For a right-angled triangle, the square of the length of the hypotenuse (the longest side) should equal the sum of the squares of the other two sides.

Let's denote the sides as:
- \( a = 2.4 \) cm
- \( b = 3.2 \) cm
- \( c = 4.0 \) cm (hypotenuse)

According to the Pythagorean theorem:
\[
c^2 = a^2 + b^2
\]

Now, let's calculate:

\[
c^2 = 4.0^2 = 16.0
\]

\[
a^2 + b^2 = 2.4^2 + 3.2^2 = 5.76 + 10.24 = 16.0
\]

Since \( c^2 = a^2 + b^2 \), these lengths do satisfy the Pythagorean theorem. Therefore, the lengths 2.4 cm, 3.2 cm, and 4.0 cm can be the sides of a right-angled triangle.

Would you like more details or have any questions?

Here are some related questions for further exploration:
1. What is the significance of the Pythagorean theorem in geometry?
2. How do you determine which side is the hypotenuse in a right-angled triangle?
3. Can a triangle have sides with fractional lengths and still satisfy the Pythagorean theorem?
4. What are the properties of an isosceles right-angled triangle?
5. How can the Pythagorean theorem be used to find the distance between two points in a plane?
6. What is the converse of the Pythagorean theorem, and how is it used?
7. Can the lengths \( 5 \) cm, \( 12 \) cm, and \( 13 \) cm form a right-angled triangle?
8. What happens if the sum of the squares of two sides is less than or greater than the square of the third side?

**Tip:** Always remember to identify the hypotenuse as the longest side when applying the Pythagorean theorem to check for right-angled triangles.

Explore if the lengths 2.4 cm, 3.2 cm, and 4.0 cm can form a right-angled triangle according to the Pythagorean theorem. Discover how to apply the theorem to determine if these side lengths can satisfy the conditions of a right triangle. Suitable for Grades 7-9 students learning about geometry and the Pythagorean theorem.

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