Question

a triangle has sides of 7 cm, 24 cm, and 25 cm. which best describes this triangle?
acute right
obtuse isosceles
acute isosceles
none of the other answer options are correct.
obtuse equilateral

Explanation:

Step1: Check for right - triangle property

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side. Let \(a = 7\), \(b=24\), \(c = 25\).
Calculate \(a^{2}+b^{2}\): \(7^{2}+24^{2}=49 + 576=625\).
Calculate \(c^{2}\): \(25^{2}=625\).
Since \(7^{2}+24^{2}=25^{2}\), it satisfies the Pythagorean theorem.

Step2: Check for side - length relationships for other types

An isosceles triangle has two equal sides. Here \(7
eq24
eq25\), so it is not isosceles.
An equilateral triangle has all three sides equal. Here \(7
eq24
eq25\), so it is not equilateral.
An acute triangle has \(a^{2}+b^{2}>c^{2}\) for all sides (where \(c\) is the longest side). But we already saw it is a right - triangle (\(a^{2}+b^{2}=c^{2}\)). An obtuse triangle has \(a^{2}+b^{2}

Answer:

None of the other answer options are correct.