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Question

# If two sides of the triangle are given as 6 cm and 16 cm, the inequality representing the range of length of third side x (in cm) is:

A
x>22
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B
x<10
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C
10<x<22
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D
6<x<16
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Solution

## The correct option is C 10<x<22Given, two sides of the triangle are 6 cm and 16 cm and the length of the third side is x cm. According to the triangle inequality theorem, the sum of two sides of a triangle is greater than the length of the third side ⇒6+16>x⇒22>x⇒x<22…(i) Also, the difference between the two sides is always smaller than the third side. ⇒16−6<x⇒10<x…(ii) From (i) and (ii), we get ⇒10<x<22 ∴ The length of the third side x will be between 10 and 22 cm.

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