At time t = 0, a set of three points A, B and C forms an equilateral triangle of side 6 cm. If two of the sides

Question

of the triangle are decreasing in length at the rate of 0.1 cm/sec and the third side is increasing at the rate of
0.1 cm/sec, how long will it take for the system to just cease to form a triangle?

Answer 1

After a time of t seconds, the lengths of the two decreasing sides are 6+.1t cm each and the side which is increasing is 6 + .1t

It will cease being a triangle if the sum of two sides equals the third side

6 + .1t = 2(6 - .1t)
6 + .1t = 12 - .2t
.3t = 6
t = 6/.3 = 20

it will take 20 seconds