Question

A shadow 15 feet long is cast by a climbing structure that is 8 feet tall. If a marble column close by casts a shadow 30 feet long, how tall is the marble column?

Answer 1

Marble column is 16 feet tall.

Explanation:

We can use similar triangles to find the height of the marble column.

In similar triangles, corresponding sides are in proportion.

Let h be the height of the marble column.

For the climbing structure:

- Height: 8 feet

- Shadow: 15 feet

For the marble column:

- Height: h feet

- Shadow: 30 feet

The proportion of the corresponding sides is:

`\sf (h)/(30) = (8)/(15)`

Now, cross-multiply to solve for h :

`\sf 15h = 8 * 30`

`\sf 15h = 240`

`\sf h = (240)/(15)`

`\sf h = 16`

Therefore, the height of the marble column is 16 feet.