Question

An isosceles triangle has a varying base b and variable legs a such that the perimeter is a differentiable function of time. Which equation best describes the relationship between the rate of change, with respect to time t, of the perimeter p and the rate of change, with respect to time t, of the base and legs of the isosceles triangle?

Answer 1

The relationship between the rate of change of the perimeter and the rate of change of the base and legs of an isosceles triangle is represented by the equation dP/dt = db/dt + 2(da/dt).

Step-by-step explanation:

The equation that best describes the relationship between the rate of change of the perimeter p of an isosceles triangle and the rate of change of its base b and legs a with respect to time t is derived using calculus and the given information about the isosceles triangle.

Since the perimeter P of an isosceles triangle with base b and equal legs a is P = b + 2a, we can find its rate of change with respect to time by differentiating both sides with respect to t, resulting in dP/dt = db/dt + 2(da/dt).