Question

pythagorean theorem converse assignment
given the side lengths below, first determine whether they form a triangle. if they do, determine whether the triangle is acute, right, or obtuse.
10, 24, 26
acute triangle
right triangle
obtuse triangle
not a triangle

Explanation:

Step1: Check Triangle Inequality

To form a triangle, the sum of any two sides must be greater than the third side.

• \(10 + 24 = 34 > 26\)
• \(10 + 26 = 36 > 24\)
• \(24 + 26 = 50 > 10\)

So, they form a triangle.

Step2: Apply Pythagorean Theorem Converse

Let \(a = 10\), \(b = 24\), \(c = 26\) (where \(c\) is the longest side).
Calculate \(a^2 + b^2\) and \(c^2\):

• \(a^2 + b^2 = 10^2 + 24^2 = 100 + 576 = 676\)
• \(c^2 = 26^2 = 676\)

Since \(a^2 + b^2 = c^2\), by the converse of the Pythagorean theorem, the triangle is a right triangle.

Answer:

Right Triangle