# Britney is 5 feet tall and casts a 3 1/2 -foot shadow at 10:00 A.M. At that time, a nearby tree casts a 17-foot shadow. Two hours later, Britney's shadow is 2 feet long. What is the length of the shadow of the tree at this time?

##### 1 Answer

The tree is (approximately) 9.71 feet tall at noon.

#### Explanation:

Because the length of an object's shadow is proportional to its height (at a given time of day), this kind of question is solved by using the proportion relation: "

#a/b = c/d#

They key to solving this question is finding the pieces of information that **(a)** give us 3 of these 4 values and **(b)** also let us use this relation to find the 4th.

What we have:

#{:(, "Britney","tree"),("height", 5, -),("10:00 shadow", "3.5 ft", "17 ft"),("12:00 shadow", "2 ft", square) :}#

The box marks what we want to solve for.

We need to use the "12:00 shadow" info, because it has the value we want to solve for. We **can not** use the height info, because it also has missing data. (We can only solve for the 4th missing piece if we have 3 of the 4 parts of the equation.)

Thus, we will use the "12:00 shadow" and the "10:00 shadow" information. We set up the ratio like this:

#"Britney's 10:00 shadow"/"Britney's 12:00 shadow" = "tree's 10:00 shadow"/"tree's 12:00 shadow"#

Let

#"3.5 ft"/"2 ft" = "17 ft"/x#

Cross-multiply:

#("3.5 ft")" " x = ("17 ft")("2 ft")#

Divide both sides by 3.5 ft:

#x = [("17 ft")("2 ft")]/("3.5 ft")#

Simplifying the right hand side gives:

#x ~~ "9.71 ft"#