Question

the side lengths of two triangles are given below.
answer the questions about each triangle.
(a) one triangle has side lengths 6, 11, and 7.
compute the sum of the squares of the shorter lengths.
6² + 7² =
compute the square of the longest length.
11² =
what kind of triangle is it?
○acute triangle
○right triangle
○obtuse triangle
(b) the other triangle has side lengths 26, 24, and 10.
compute the sum of the squares of the shorter lengths.
10² + 24² =
compute the square of the longest length.
26² =
what kind of triangle is it?
○acute triangle
○right triangle
○obtuse triangle

Explanation:

Step1: Calculate \(6^{2}+7^{2}\)

$$
LATEXBLOCK0
$$

Step2: Calculate \(11^{2}\)

$$11^{2}=121$$

Since \(85<121\) (\(a^{2}+b^{2}

Step3: Calculate \(10^{2}+24^{2}\)

$$
LATEXBLOCK1
$$

Step4: Calculate \(26^{2}\)

$$26^{2}=676$$

Since \(10^{2}+24^{2}=26^{2}\) (\(a^{2}+b^{2}=c^{2}\)), the triangle is right - angled.

Answer:

(a) \(6^{2}+7^{2}=85\), \(11^{2}=121\), Obtuse triangle.
(b) \(10^{2}+24^{2}=676\), \(26^{2}=676\), Right triangle.