Question

1. 10, 24, 26

not a δ
acute
right
obtuse

Explanation:

Step1: Check if it's a triangle

Use the triangle - inequality theorem. For three side - lengths \(a = 10\), \(b = 24\), \(c = 26\), we need to check \(a + b>c\), \(a + c>b\), and \(b + c>a\).
\(10+24 = 34>26\), \(10 + 26=36>24\), \(24 + 26 = 50>10\). So, it is a triangle.

Step2: Determine the type of triangle

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) for right - triangles, where \(c\) is the longest side.
\(a = 10\), \(b = 24\), \(c = 26\). Calculate \(a^{2}+b^{2}\): \(10^{2}+24^{2}=100 + 576=676\).
Calculate \(c^{2}\): \(26^{2}=676\). Since \(10^{2}+24^{2}=26^{2}\), it is a right - triangle.

Answer:

Right