The sides of a triangle have lengths K, 11, and 15, such that K is an integer. What is the total number of values of K for which the triangle will be possible?
A) 22
B) 23
C) 21
D) 25
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The total number of values of K is 21
Step-by-step explanation:
Given,sides of a triangle = K, 11, 15
We know that,
In a triangle
Sum of two sides > third side
Difference of two side < third side
⇒11 + 15 > K
⇒26 > k........(1)
Also, 15 - 14 < K
4 < K..........(2)
From (1) and (2)
4 < K < 26
⇒Value of third side will lie in between 4 and 26.
Hence, the total possible value of third side can be 26 - 4 = 21.
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