Question

Becky casts a 7-foot shadow at the same time a nearby mailbox casts a 4-foot shadow. If the mailbox is 3 feet tall, how tall is Becky? Express your answer as a decimal if necessary.

Answer 1

To determine Becky's height, we can use the concept of similar triangles, where the ratios of corresponding heights and shadow lengths are equal.

Let \( h \) be Becky's height in feet. From the problem, we have the following information:

- Height of the mailbox: \( 3 \) feet
- Shadow length of the mailbox: \( 4 \) feet
- Shadow length of Becky: \( 7 \) feet

Using the property of similar triangles, we can set up the following equation based on the ratios of height to shadow length:

\[
\frac{h}{7} = \frac{3}{4}
\]

To solve for \( h \), we can cross-multiply:

\[
4h = 21
\]

Now, divide both sides by \( 4 \):

\[
h = \frac{21}{4}
\]

Calculating this gives:

\[
h = 5.25
\]

Thus, Becky's height is

\[
\boxed{5.25} \text{ feet}.
\]