The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3 cm per second. How fast is the area decreasing when the two equal sides are equal to the base?

Question

Philoid · Accepted Answer

Let ΔABC be isosceles where BC is the base of fixed length b.

Let the length of the two equal sides of ΔABC be a.

Now, draw a perpendicular AD to BC. Then, we have

In ΔADC, by using Pythagoras theorem,

AD =

Then, Area of triangle (A) =

The rate of change of the area with respect to time (t) is given by:

It is given that the two equal sides of the triangle are decreasing at the rate of 3cm per second.

Then

And when a = b we have,

Therefore, if the two sides are equal to the base, then the area of the triangle is decreasing at the rate of cm²/s.