Question

Now, show that AB + BC + AC < 2 (OA + OB + OC).
The length of two sides of a triangle are 4 cm and 6 cm. Between what two measure
should the length of the third side fall?​

Answer 1

Answer:

Making a triangle is possible only with sides given in option ‘b’. In other options, sum of two sides is either equal to or less than the third side.

Question 2: Take any point O in the interior of a triangle PQR. Is

triangles

OP + OQ > PQ?

OQ + OR > QR?

OR + OP > RP?

Answer: The answer is yes in each case, because sum of any two sides of a triangle is always greater than the third side.

Question 3: AM is a median of a triangle ABC. Is AB + BC + CA > 2AM? (Consider the sides of ΔABM and ΔAMC)

triangles

Answer: In ΔABM; AB + BM > AM

Similarly, in ΔAMC; AC + CM > AM

Adding above equations, we get;

AB + BM + CM + AC > 2AM

Or, AB + BC + CA > 2AM