Question

Sides of Similar Figures Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
4 of 54 of 5 Items







Question
A person 5 ft. tall is standing near a building 30 ft. high. If the length of the person’s shadow is 3 ft., what is the length of the shadow of the building?(1 point)
ft.

Answer 1

To solve the problem, we can use the concept of similar figures. The ratio of the heights of the person and the building will be equal to the ratio of the lengths of their shadows.

Let \( h_1 = 5 \) ft (height of the person), \( h_2 = 30 \) ft (height of the building), \( s_1 = 3 \) ft (length of the person's shadow), and \( s_2 \) be the length of the shadow of the building.

Using the property of similar triangles, we can set up the following proportion:

\[
\frac{h_1}{h_2} = \frac{s_1}{s_2}
\]

Substituting the known values into the equation:

\[
\frac{5}{30} = \frac{3}{s_2}
\]

To solve for \( s_2 \), we can cross-multiply:

\[
5 \cdot s_2 = 30 \cdot 3
\]

This simplifies to:

\[
5s_2 = 90
\]

Now, divide both sides by 5:

\[
s_2 = \frac{90}{5} = 18
\]

Thus, the length of the shadow of the building is \( \text{18 ft} \).