__Triangle Inequality Theorem:__
Sum of two sides of a
triangle must be greater than the measure of the third side

a + b > c
b + c > a
a + c > b

Q1) Given Integers as the
lengths of sides of a triangle. Find the maximum and minimum perimeter of the
triangle where two of the sides measure 9 and 5?

__Solution:__

__To find maximum perimeter__

Sum of the lengths of given
sides = 9+5 = 14

Hence maximum length of the
third side = 13

(This can be understood
from Triangle inequality theorem)

Maximum perimeter = 9+5+13
=27

__To find minimum perimeter__

For finding minimum
perimeter, we can consider 9 as the length of longest side.

As the given sides are 5
and 9, let us consider the third side between 1 and 5.

For meeting the triangle
inequality rule, we cannot consider 1 to 4.

Hence the minimum value to
be considered for the third side = 5, in which case the three sides

measure 5, 5 and 9

(Test triangle inequality
rule:
5+5>9
5+9>5 9+5>5)

Minimum perimeter = 5+5+9 =
19

The perimeter of the given
triangle ranges between 19 and 27

Q2) Which of the following sets of sides won’t form a triangle?

(A)3,3,4
(B)3,4,5
(C)3,4,6
(D)3,4,7
(E)2,3,4

__Solution:__

This is an application of Triangle Inequality
rule. Check this rule for the given options one by one. For option D, 3+4
= 7, this is equal to the third side but not more than that. It's violation of the
rule. Hence Answer option is (D)

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