Decide if the following could be sides of a triangle (yes or no). If yes, classify the triangles as acute, obtuse, or right. **Question 14**: Given the side lengths 7, 7√2, and 7.Use these lengths to classify the type of triangle.### Explanation:To classify the triangle, we can compare the side lengths:1. The given side lengths are 7, 7√2, and 7.2. Notice that two sides are equal (7 and 7), making this an isosceles triangle.3. Additionally, we can determine if this triangle is a right triangle by using the Pythagorean theorem. - For a triangle to be a right triangle, the square of the length of the longest side (hypotenuse) should equal the sum of the squares of the lengths of the other two sides. - Here, let's check the relation: - Longest side (hypotenuse) = 7√2 - Other two sides = 7 and 7 \[(7√2)^2 = 7^2 + 7^2\] \[49 * 2 = 49 + 49\] \[98 = 98\] The equation holds true, so the given side lengths form a right triangle.### Conclusion:- This is an **Isosceles Right Triangle**, since it has two equal sides and it satisfies the Pythagorean theorem.

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Answered: YES, classify the triangles 14.)…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Decide if the following could be sides of a triangle (yes or no). If yes, classify the triangles as acute, obtuse, or right.

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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