Respuesta :
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: 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
[tex]5+10>x\\\\\Rightarrow x<15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
[tex]5+x>10\\\\\Rightarrow x>5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
and
[tex]x+10>5\\\\\Rightarrow x>-5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
From inequalities (i), (ii) and (iii), we get
[tex]5<x<15.[/tex]
Thus, the length of the third side is greater than 5 and less than 15 units.
