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Joey found that an elm tree that is 8 feet tall casts a shadow 15 feet long. Then Joey noticed that a jungle gym nearby casts a shadow 30 feet long. How tall is the jungle gym? Write your answer as a whole number or a decimal. Do not round.

Ask by Perkins Patel. in the United States
Jan 23,2025

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Answer

The jungle gym is 16 feet tall.

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The Deep Dive

To solve this, we can use the concept of similar triangles. The height of the elm tree and its shadow can be set up in a proportion with the jungle gym and its shadow. If we denote the height of the jungle gym as "h", we can set up the ratio as follows: \[ \frac{8 \text{ feet (height of elm tree)}}{15 \text{ feet (shadow of elm tree)}} = \frac{h \text{ (height of jungle gym)}}{30 \text{ feet (shadow of jungle gym)}} \] Cross-multiplying gives us: \[ 8 \times 30 = 15 \times h \] This simplifies to: \[ 240 = 15h \] Now, divide both sides by 15: \[ h = \frac{240}{15} = 16 \] Thus, the height of the jungle gym is 16 feet.

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