HSC Mathematics Standard 2 Practice Exam

Question: 1 / 400

If a triangle has sides of 7 cm, 8 cm, and 5 cm, is it a right triangle?

Yes

To determine whether a triangle with sides measuring 7 cm, 8 cm, and 5 cm is a right triangle, we can apply the Pythagorean theorem. This theorem states that for a triangle to be a right triangle, the square of the length of the longest side (hypotenuse) should equal the sum of the squares of the other two sides.

In this case, the longest side is 8 cm. We can calculate:

1. The square of the longest side: \(8^2 = 64\).

2. The squares of the other two sides: \(7^2 = 49\) and \(5^2 = 25\).

3. Sum of the squares of the other two sides: \(49 + 25 = 74\).

Now we check if the square of the longest side equals the sum of the squares of the other sides:

- \(64\) (the square of the longest side) is not equal to \(74\) (the sum of the squares of the other two sides).

Since this condition does not hold, the triangle is not a right triangle. Therefore, the correct answer to the question is "No," indicating that the triangle with sides of 7

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No

It cannot be determined

Only if it's acute

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