The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3 cm per second.

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asked Jan 23, 2018 in Mathematics by sforrest072 (157,439 points) 61 410 940
edited Jan 23, 2018 by sforrest072

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?

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answered Jan 23, 2018 by mdsamim (213,225 points) 5 10 15
selected Jan 23, 2018 by sforrest072
 
Best answer

Let ABC be isosceles where BC is the base of fixed length b.
Let the length of the two equal sides of ABC be a.
Draw AD BC.

Now, in ADC, by applying the Pythagoras theorem, we have:

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 3 cm per second.

Hence, if the two equal sides are equal to the base, then the area of the triangle is decreasing at the rate of 

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