Question

Is it possible to construct a triangle with sides 9 cm, 6 cm and 17 cm? If not, why?

Answer 1

Hint: As we can see, 9+6 = 15 which is less than the third side. We know that if the sum of the two smaller sides is equal or more than the third side then the construction of the triangle is possible, but here the sum is less so the triangle cannot be constructed.

Complete step-by-step answer:
We know that the sum of any 2 sides of a triangle should be greater than the third side.
Let A=9 cm, B=6 cm and C=17 cm.
So, here
A+B should be greater than C
Now, A+B= 9+6=15 cm
               C=17 cm
Since, $A+B$<$C$
The construction of the given triangle is not possible.
So, in this question construction of a triangle is not possible with sides A=9 cm, B=6 cm and C=17 cm.

Note: It is possible to draw more than one triangle that has three sides with the given lengths. For example, in the figure below, given the base AB, you can draw four triangles that meet the requirements. All four are correct in that they satisfy the requirements, and are congruent to each other.

But construction is not always possible, if two sides add to less than the third, no triangle is possible.