Q. 34.4( 20 Votes )
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?
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.
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