# How high is a tree that casts a 22-ft shadow at the same time a 4-ft post casts a shadow that is...

## Question:

How high is a tree that casts a 22-ft shadow at the same time a 4-ft post casts a shadow that is 6-ft long?

## Proportions:

Using proportions is the tool used to balance the reactants and products in stoichiometry. In chemistry, stoichiometry uses the relationships between the reactants and products as the guide in balancing a chemical reaction and making sure that the proportions follow the law of conservation of mass.

The tree casts a 22-ft shadow at the same time that a 4-ft post casts a 6-ft shadow, using the information to make a proportion, the height of the tree can be determined by solving for it:

{eq}\begin{align} \rm \dfrac {x \ height \ of \ tree}{ 22 \ feet \ shadow} &= \rm \dfrac { 4 \ feet \ height \ of \ post}{6 \ feet \ shadow} \\ \dfrac x {22} &= \dfrac 4 6 \\ x &= \dfrac{4(22)}{6} \\ x &= \dfrac {88}{6} \\ x &= 14 \dfrac 4 6 \\ x &= 14 \dfrac 2 3 \end{align} {/eq}

The tress is {eq}14 \dfrac 2 3 \rm \ feet {/eq} high. 