Question

Question:- Three line segments have measurements of 7cm, 8cm, 9cm. Will the segments from a triangle?

Answer 1

Answer:

sides= 7cm, 8cm, 9cm.

the longest side is the hypotenuse and the shortest side is the base..

so using Pythagoras theorem

9² should be equal to 7²+ 8²

9²= 81

and 7²+8²= 49 + 64= 113

81 is not equal to 113 ..

thus ..the triangle with such dimensions is not possible..

Answer 2

Given : ↴

$\sf \: Sides \: \longrightarrow 7cm, \: 8cm, 9cm.$

To find : ↴

$\sf \: Whether \: these \: line \: segments \: form \: a \: triangle \: or \: not.$

So, Let's Start : ↴

$\sf \: Property \: to \: be \: used \: here :$ ↴

$\boxed{ \sf \: The \: sum \: of \: two \: sides \: of \: a \: \triangle \: \: \boxed> \: third \: side.}$

$\sf \: Here \: the \: Sides \: are \: 7cm, \: 8cm, \: 9cm.$

$\sf \: So, \: According\: to\:the\: Formula$ ↴

$\boxed { \sf \: 7 \: + \: 8 \: \: \boxed> \: 9}$

${\sf \:15 \: \: \boxed> \: 9}$

$\sf \: Here \: 7 \: + \: 8 \: is \: greater \: than \: 9.$

$\sf \: So, \: Hence \: it \: will \: form \: a \: \triangle.$

Extra information : ↴

A triangle is a simplest form of polygon and it have three sides in it.

Properties of Triangle : ↴

(1). A triangle always have three sides, three angles, and three vertices.

(2). The sum of the length of any two sides of a triangle is always greater than the length of the third side. (Angle sum property of a triangle)

(3). The sum of all internal angles of a triangle is always equal to 180°.

4). The side opposite to the largest angle of a triangle is the largest side.

(5). Any exterior angle of the triangle is equal to the sum of its interior opposite angles. (Exterior angle property of a triangle)