Apply the Pythagorean Theorem to determine whether a triangle with sides 10 cm, 24 cm, and 25 cm is a right triangle.

Question

Responses

The triangle is not a right triangle because 10^2+24^2≠25^2

The triangle is a right triangle because 10^2+24^2=676

The triangle is not a right triangle because 10+24≠25

The triangle is a right triangle because 10+24=25+9.

Answer 1

To determine whether a triangle with sides 10 cm, 24 cm, and 25 cm is a right triangle, we can use the Pythagorean Theorem. The theorem 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 sides are:

• a = 10 cm
• b = 24 cm
• c = 25 cm (hypotenuse)

Now we can apply the Pythagorean theorem:

\(c^2 = a^2 + b^2\)

Calculating each side:

• \(c^2 = 25^2 = 625\)
• \(a^2 = 10^2 = 100\)
• \(b^2 = 24^2 = 576\)

Now, let's add \(a^2\) and \(b^2\):

\(a^2 + b^2 = 100 + 576 = 676\)

Now we compare:

• Since \(625 ≠ 676\), it follows that \(c^2 ≠ a^2 + b^2\).

Thus, the triangle is not a right triangle.

The correct response is:

The triangle is not a right triangle because \(10^2 + 24^2 ≠ 25^2\).