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Triangle Inequality Theorem

x is an integ...

Question

x is an integer greater than 16. Find the value of x - 10, if x is the length of the side AC of the triangle given below.

A

7

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B

17

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C

10

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D

18

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Solution

The correct option is A 7
Given, x is the length of one of the sides of $Δ A B C$ .
We know that the sum of any two sides of a triangle is always greater than the third side.
$\Rightarrow$ 10 + 8 > x
$\Rightarrow$ 18 > x
i.e., x < 18.
It is also given that x is an integer greater than 16.
So, the only possible value of x is 17.
$∴$ x - 10 = 17 - 10 = 7.

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