Question

"The side of an equilateral triangle decreases at the rate of 2 cm/s. At what rate is the area decreasing when the area is 100 cm^2?"

Help!

Answer 1

let each side be x cm
given: dx/dt = -2 cm/s
find: dA/dt when A = 100

by the 30-60-90 triangle the height of the triangle will be (√3/2)x . You can also use Pythagoras to find that.

Area of triangle = (1/2)(x)(√3x/2)
= (√3/4)x^2
when A = 100
(√3/4)x^2 = 100
x^2 = 400/√3
x = 20/√(√3) = 15.1967

dA/dt = (√3/2)x dx/dt
= (√3/2)(15.1967)(-2)
= -26.32 cm^2/s

check my arithmetic

Answer 2

Thank you!!

Answer 3

Thank you very much . This is the answer I got as well; however it is different than the answer given in the text which is 11.5 cm squared/sec. Thank you again.

Answer 4

Thanks for this answer. I must have the same sheet, it also had 11.5 cm/s answer. I kept getting 26.32 cm/s and I couldn't figure out why...

Answer 5

I love you Reiny

Answer 6

How do you get the height of the triangle, I don't understand. can you explain it in more detail?