Question

Determine which three lengths can be the measure of the sides of a triangle.
a) 14cm, 3cm, 18cm

b) 9cm, 7cm, 15cm

c) 2cm, 14cm, 18cm

d) 6cm, 9cm, 15cm

Answer 1

Answer:

d) 6cm, 9cm, 15cm

Step-by-step explanation:

because of 6cm+9cm= 15 cm and third side is also a 15 cm Soo that's y..

Answer 2

$\bf \underline{ \underline{Understanding \: the \: concept : } }$

Here, in this question different lengths are given and we have to determine that which three lengths can be the measure of the sides of a triangle.

$\bf \underline{ \underline{We \: know \: that : } }$

The sum of the length of any two sides of a triangle is always greater than the length of the third side. [Triangle inequality theorem]

$\bf \underline{ \underline{Solution : } }$

$\bf \: a) \: 14 \: cm, \: 3 \: cm, \: 18 \: cm$

$\sf \implies 14 \: cm + 3 \: cm = 17 \: cm$

$\sf \implies 17 \: cm \: < 18 \: cm$

$\sf \underline{ Hence, triangle \: can't \: be \: formed. }$

$\bf\: b) \: 9 \: cm, \: 7 \: cm, \: 15 \: cm$

$\sf \implies 9 \: cm + 7\: cm = 16\: cm$

$\sf \implies 16 \: cm \: > 15 \: cm$

$\sf \underline{ Hence, triangle \: can \: be \: formed. }$

$\bf \: c) \: 2 \: cm, \: 14 \: cm, \: 18 \: cm$

$\sf \implies 2 \: cm + 14 \: cm = 16 \: cm$

$\sf \implies 16 \: cm \: < 18 \: cm$

$\sf \underline{ Hence, triangle \: can't \: be \: formed. }$

$\bf \: d) \: 6 \: cm, \: 9 \: cm, \: 15 \: cm$

$\sf \implies 6 \: cm + 9 \: cm = 15 \: cm$

$\sf \implies 15 \: cm \: = 15 \: cm$

$\sf \underline{ Hence, triangle \: can't \: be \: formed. }$

$\bf \underline{Therefore},$

$\sf \implies 2^{nd} \: option \: is \: correct..$

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$\bf \: \underline{ Extra\: information}\::$

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

$\bf \: \underline{\underline{Properties \: of \: Triangle :}}$

(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. [Triangle inequality theorem]

(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)