Question

Find all possible lengths of the third side, if sides of a triangle have $2$ and $5$.

• A. $2<x<7$
• B. $3>x<7$
• C. $3<x>7$
• D. $3<x<7$

Answer 1

The correct option is D $3<x<7$

The Triangle Inequality theorem states that the sum of any $2$ sides of a triangle must be greater than the measure of the third side.
So, difference of two sides $<x<$ sum of two sides, will give you the possible length of a triangle.
Therefore, $5-2<x<5+2$
$3<x<7$ is the possible length of the third side of a triangle.
For checking the possible length: Take $2,5,4$
$2+5>4(a+b>c)$
$5+4>2(b+c>a)$
$2+4>5(a+c>b)$
Hence, the above condition satisfied the triangle inequality theorem.