Need help please---Dealing with similar triangles.

[wildcat13]

I am super lost on this problem. In geometry, we are on a section about similar triangles and are given this problem: A light shines on a wall. A 12 inch ruler is held parallel to the wall between the light and the wall. If the ruler is 7 feet from the light bulb and 18 feet from the wall, how long is its shadow?

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[soroban]

Hello, wildcat13!

I don't suppose you made a sketch . . .

A light shines on a wall.
A 12-inch (1-foot) ruler is held parallel to the wall between the light and the wall.
If the ruler is 7 feet from the light bulb and 18 feet from the wall, how long is its shadow?

      : - - 7 - - : - - - 18  - - - :
                                    * D
                              *     |
                  B     *           |
                  *                 |
            *     |                 |
    A o           |1                | s
            *     |                 |
                  *                 |
                  C     *           |
                              *     |
                                    * E

The light is at \(\displaystyle A.\)
The ruler is: \(\displaystyle BC = 1.\)
The shadow is: \(\displaystyle DE = s.\)

We have two similar triangles: .\(\displaystyle \Delta ABC\,\sim\,\Delta ADE\)
Their bases are \(\displaystyle 1\) and \(\displaystyle s.\)
Their altitudes are \(\displaystyle 7\) and \(\displaystyle 25.\)

We have: .\(\displaystyle \dfrac{s}{25} \,=\,\dfrac{1}{7} \quad\Rightarrow\quad s \,=\,\dfrac{25}{7}\)

Therefore, the length of the shadow is: .\(\displaystyle s \:=\:3\frac{4}{7}\) feet.

 

[wildcat13]

Thank you somuch!!