# Thread: Related Rates Similar Triangles

1. ## Related Rates Similar Triangles

While in Wonderland, Alice eats a cookie that makes her grow taller at a rate of 0.5 ft/min. She is standing 40 feet away from a light which is 20 feet tall. How fast is the length of her shadow changing when she is 15 feet tall?

I know that this is a similar triangles problem and you have to cross-multiply the ratios, but that's all that I know. Can someone please help me? Thank you so much!

2. Let "x" be Alice's height and "y" be the length of her shadow. Then using similar triangles, as you say, should give $\displaystyle \frac{y}{x}= \frac{y+ 40}{20}$. "Cross multiplying" you get $\displaystyle 20y= x(y+ 40)$.

Now differentiate both sides with respect to time, "t", to get an equation relating $\displaystyle \frac{dx}{dt}$ and $\displaystyle \frac{dy}{dt}$. You are told that $\displaystyle \frac{dx}{dt}= 0.5$ and are asked to find $\displaystyle \frac{dy}{dt}$ when y= 15.

3. Wow, you make it so simple! All my friends complicated it and just confused me even more. Thank you so much, you have no idea.. you saved my life lol!