Chapter 1.3, Problem 40E

To determine

To draw different figure with same perimeter as the triangle shown and explain

Explanation of Solution

Given:

  

Formula Used:

Perimeter is equal to the sum of all the sides of the given figure.

Let, $x=3$

  

Then, the values are of the sides are:

  $\begin{array}{l}x+3=3+3=6\\ 3x=3\times 3=9\\ 2x+1=2\times 3+1=7\end{array}$

Therefore the figure considering the above length of sides becomes:

  

The perimeter of the triangle will be $=6+7+9=22$

The figure with same perimeter is as such:

  

From the above figure, it is clear that, the new triangle is completely different from the one given in the question, but still the perimeter is same.

That means by changing the angles and length of sides, infinite number of triangles can be obtained by keeping the perimeter constant.

Conclusion:

Therefore, by changing the angles and length of sides, infinite number of triangles can be obtained by keeping the perimeter constant