If a 40 foot tree cast a 16 foot shadow, what is the length of the shadow cast by a 27 foot tree?

I take it that we are to assume that the ratio between the actual length and the shadow length are directly proportional

so therefor we set up the following proprtion

actual height: shadow height=40ft:16ft

we are given that the tree is actually 27ft

so

40ft:16ft=27ft:? ft

make into a fraction

40ft/16ft=27ft/? ft

cross multiply or multiply both sides by 16? ft²

40? ft²=432ft²

divide both sides by 40ft

? ft=10.8ft

the length of the shadow is therfore 10.8ft

this is a ratio:

40/16 = 27/x

cross multiply:

40x = (16*27) =

40x=432

x = 432/40 = 10.8 feet