Question

A 6 ft tree casts a 21 ft shadow. How
tall is a tree which casts a 49 ft shadow?

Answer 1

14 ft

Givens

We are given that a 6 ft tall tree casts a 21 ft shadow. We can assume this relationship is proportional, and as such, we can relate this to another tree of an unknown height that is casting a 49 ft shadow. To do this, we need to create a proportion that helps us solve for the unknown tree's height.

Solve

To begin, create a proportional relationship between the two trees, where x is the height of the tree with a 49 ft shadow:

`\displaystyle (6)/(21)=(x)/(49)`

Then, cross-multiply the two proportions to create an equation that can be solved for the variable x:

`\displaystyle 6*49=294\\\\21* x=21x\\\\294=21x`

Then, divide both sides of the equation by 21 to isolate the variable:

`\displaystyle (294)/(21)=(21x)/(21)\\\\x=14`

Therefore, the tree that casts a 49 ft shadow is 14 ft tall.