High School

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A tree in the schoolyard casts a 60-inch shadow at the same time a nearby student casts a 17-inch shadow. If the student is 68 inches tall, how many feet tall is the tree?

Answer :

The tree is 20 feet tall.

To solve this problem, we'll use proportions. Proportions allow us to compare the relationship between different lengths or quantities.

Let's define the heights and shadows:

Height of the student (h): 68 inches

Height of the tree (h_tree): unknown

Length of the student's shadow (s): 17 inches

Length of the tree's shadow (s_tree): 60 inches

We'll set up a proportion to find the height of the tree:

[tex]\( \frac{h}{s} = \frac{h_{tree}}{s_{tree}} \)[/tex]

Plugging in the values we know:

[tex]\( \frac{68}{17} = \frac{h_{tree}}{60} \)[/tex]

Now, let's solve for [tex]\( h_{tree} \)[/tex]:

[tex]\( h_{tree} = \frac{68 \times 60}{17} \)[/tex]

[tex]\( h_{tree} = \frac{4080}{17} \)[/tex]

[tex]\( h_{tree} = 240 \)[/tex] inches

To convert inches to feet, we divide by 12 (since 12 inches = 1 foot):

[tex]\( h_{tree} = \frac{240}{12} \)[/tex] feet

[tex]\( h_{tree} = 20 \)[/tex] feet

So, the tree is 20 feet tall.

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Rewritten by : Barada