Question

A triangle has sides with lengths of 10 meters, 16 meters and 20 meters. Is it a right angled triangle? Explain your reasoning.

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1. Identify the side lengths:

a = 10, b = 16, c = 20.

2. Apply the Pythagorean theorem to check if the triangle is right-angled:

a^2 + b^2 = c^2.

3. Compute the squares of each side:

10^2 = 100,

16^2 = 256,

20^2 = 400.

4. Add the squares of the two shorter sides:

100 + 256 = 356.

5. Compare this sum to the square of the longest side:

356 \neq 400.

The triangle is not a right-angled triangle.

2. Apply the Pythagorean theorem to check if the triangle is right-angled:

3. Compute the squares of each side:

4. Add the squares of the two shorter sides:

5. Compare this sum to the square of the longest side:

The triangle is not a right-angled triangle.

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