Question

If the lengths of two sides of a certain triangle are 5 and 10, what is the length of the third side of the triangle?

Answer 1

Answer:

Step-by-step explanation:

let x be the length of third side.

10-5<x<10+5

or 5<x<15

so third side is between 5 and 15 .

Answer 2

Answer:  The length of the third side is greater than 5 and less than 15 units.

Step-by-step explanation: Given that the lengths of two sides of a certain triangle are 5 and 10 units.

We are to find the length of the third side of the triangle.

Let x represents the length of the third side of the given triangle.

We know that the sum of the lengths of two sides of a triangle is always greater than the length of the third side, so we must have

$5+10>x\\\\\Rightarrow x<15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

$5+x>10\\\\\Rightarrow x>5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

and

$x+10>5\\\\\Rightarrow x>-5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

From inequalities (i), (ii) and (iii), we get

$5<x<15.$

Thus, the length of the third side is greater than 5 and less than 15 units.