A 9-foot-tall sapling casts a shadow 2.5 feet long. At the same time, an old pine tree casts a shadow 20 feet long. How many feet tall is the pine tree?

Question

mathmale · Answer

Hi, Faizah,
I'd suggest you set up an equations of ratios.  
The ratio of the length of the shadow of the sapling (young tree) to that of the length of the shadow of the the old tree is what?

Similarly, the ratio of the height of the sapling to that of the old tree is what?  Hint:  choose a letter (a literal) to represent the height of the old tree.

equate these two ratios.

Solve for the unknown.

anonymous · Answer

You mean Ill make young tree's shadow and the old tree shadow's ratio...and and then how come ill construct an equation after that? @mathmale

anonymous · Answer

$$9/m=2.5/20$$

anonymous · Answer

Is this right?

mathmale · Answer

Beautiful!  Please go ahead and solve for m.  Hint:  Cross-multiply.

mathmale · Answer

Your ratio is fine and will produce the correct answer (m, the height of the old tree).
However, I'd still suggest that you write a ratio of the tree heights, another ratio of the shadow lengths, and then equate these ratios:$$\frac{ 2.5 }{ 20 }=\frac{ 9 }{ m }$$

anonymous · Answer

Omg! I did it! Thankyou so much...u r awesome ^_^

mathmale · Answer

Thanks very much!  So glad you were able to find the right answer.  Hope to work with you again!

anonymous · Answer

Me too ^_^