Question

question 24 of 25

a triangle with sides of lengths 10, 24, and 27 is a right triangle.

a. true

b. false

Explanation:

Identify the side lengths

We are given a triangle with side lengths \(a = 10\), \(b = 24\), and \(c = 27\). The longest side, which would be the hypotenuse if it is a right triangle, is \(c = 27\).

Apply the Pythagorean Theorem

Using the Pythagorean Theorem knowledge point

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Calculate the square of the longest side

We calculate the square of the longest side \(c\):

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Compare the values

We compare the sum of the squares of the two shorter sides to the square of the longest side:

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Since \(a^2 + b^2
eq c^2\), the triangle does not satisfy the converse of the Pythagorean theorem and is not a right triangle. Therefore, the statement is false.

Answer:

• A. True
• B. False (Correct answer)