Question

Sides of Similar Figures Practice
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Question
A certain tree casts a shadow 6 m long. At the same time, a nearby man measuring 2 m tall casts a shadow 4 m long. What is the height of the tree?(1 point)

Answer 1

To find the height of the tree using the properties of similar figures, we can set up a proportion based on the heights and the lengths of the shadows.

Let \( h \) be the height of the tree. The ratio of the height of the man to the height of the tree should be equal to the ratio of the length of the shadow cast by the man to the length of the shadow cast by the tree.

This can be expressed as:

\[
\frac{\text{height of man}}{\text{height of tree}} = \frac{\text{length of man's shadow}}{\text{length of tree's shadow}}
\]

Plugging in the values:

\[
\frac{2 \, \text{m}}{h} = \frac{4 \, \text{m}}{6 \, \text{m}}
\]

Now we can cross-multiply to solve for \( h \):

\[
2 \cdot 6 = 4 \cdot h
\]

\[
12 = 4h
\]

Now, divide both sides by 4:

\[
h = \frac{12}{4} = 3 \, \text{m}
\]

Therefore, the height of the tree is **3 meters**.