Question

The lengths of two sides of a triangle are $7$ cm and $10$ cm. What is the possible value range of the third side?

• A. $3$ cm $<$ third side $<10$ cm
• B. $7$ cm $<$ third side $<10$ cm
• C. $3$ cm $<$ third side $<17$ cm
• D. $7$ cm $<$ third side

Answer 1

The correct option is C $3$ cm $<$ third side $<17$ cm

We know that:
(i) The sum of lengths of any two sides of a triangle is greater than the third side. Thus, we know that $(7+10)$ cm is greater than the third side.
Therefore, third side is less than $17$ cm.
(ii) The difference of lengths of any two sides of triangle is smaller than the third side. Thus $(10-7)cm$ is smaller than the third side.
Therefore, third side is greater than $3$ cm
Thus, $3$ cm $<$ third side $<17$ cm.