Question

if two triangles are 8cm and 13cm then the third side lies​

Answer 1

Hello Mate..
Is 13 hypotonous or side???
The question should be a bit more informative..
Sorry..

Answer 2

Answer: Between 5 cm and 21 cm internally.

We are familiar with the concept that a triangle can be drawn if the largest among the three sides for a triangle is smaller than the sum of the other two sides.

This means, if a, b, c are sides of a triangle and c is the largest, then it is always true that c < a + b.

Here, lengths of two sides of a triangle are given, 8 cm and 13 cm.

To find the lowest possible value for the length of the third side, we have to consider the larger side among the given, i.e., 13 cm, as the 'largest' side of the triangle.

Let the third side be k, so that,

$\begin{aligned}13 &< 8 + k \\ \\ 13-8 &< k \\ \\ 5 &< k\end{aligned}$

Seems that the value of k, i.e., the length of the third side, is greater than 5 cm. Thus we can say that the lowest possible value for the length of the third side is greater than 5 cm.

[Note: Don't say that the lowest possible value is 6 cm, because the length of the third side can be 5.1 cm, 5.01 cm, 5.001 cm, or any much! They are greater than 5, aren't they?!]

Now we have to find the highest possible value for the length of the third side. Here the other sides are 8 cm and 13 cm, whose sum should be greater than the third side.

Let the third side also be k, such that,

$k <8+13 \\ \\ k<21$

Seems that the value of k, i.e., the length of the third side, is lesser than 21 cm. Thus we can say that the highest possible value for the length of the third side is lesser than 21 cm.

[Note: Don't say that the highest possible value is 20 cm, because the length of the third side can be 20.9 cm, 20.99 cm, 20.999 cm, or any much! They are lesser than 21, aren't they?!]

Hence, the answer is,

$\Huge 5<k<21$

where k is the length of the third side.