Math Calculas 1

Question

The height of an equilateral triangle is decreasing at a rate of 0.5 centimeters per second. Find the rate of change of the area of the triangle when its height is 6 centimeters.



Answer 1

Let x = the length of each side of the triangle

The relationship between the height and the base is, h² = x² - x²/4 = 3x²/4 ---> x = 2h/√3

The area is one half base time height, A = hx/2 = h(2h/√3)/2 = h²/√3

dA/dt = 2h(dh/dt)/√3

When h = 6 and dh/dt = -1/2, dA/dt = 12(-1/2)/√3 = -6/√3 = -2√3 cm/s

The area is decreasing at 2√3 cm/s