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4 years ago

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?

Mathematics

2 answers:

USPshnik [31]4 years ago

7 0

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

$5+10>x\\\\\Rightarrow x$

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

and

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

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

$5$

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

lina2011 [118]4 years ago

5 0

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 .

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