Answered: A triangle has two sides with length…

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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A triangle has two sides with length 14inch and 30 inch . what length would be the third side of the triangle in inch.

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°).

Expert Solution

Step 1

Given a triangle whose two sides with length 14 inch and 30 inch.

We know that sum of length of any two sides of a triangle is greater than the length of third side.

So, length of third side would be such that if we add any two sides then sum is greater than third side.

Let third side be $x$ then:

$\begin{array}{rcl} 14 + x & > & 30 \\ x & > & 30 - 14 \\ x & > & 16 \end{array}$

Therefore, length of third side should be greater than 16 inch.

Suppose we take third side as 17 inch.

So, if we add any two sides then it will be will be greater than third side.

$14 + 17 = 31 > 30$

14+30=44>17

30+17=47>14

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