fifth grade geometry

[cwoo]

I am a parent trying to help my daughter study for a test. She is doing a practice test with problems concerning finding the missing side with similar triangles. The problem is:

The first triangle's left side is 25m and the other side is 32m
The second triangle's first side is 10m and the other side is x.
I know that there has to be a certain equation to find what x is but I have no earthly idea what it is...please help!

 

[tkhunny]

There we go. An actual problem statement.

First: 25 * 32 * SomethingMissing

Second: 10 * x * OtherMissing

If these are similar triangles, then corresponding parts have identical ratios.

25 / 10 = 2.5

32 / x = 2.5

SomethingMissing / OtherMissing = 2.5

 

[soroban]

Hello, cwoo!

The first triangle's left side is 25m and the other side is 32m.
The second triangle's first side is 10m and the other side is x.
I know that there has to be a certain equation to find what x is
but I have no earthly idea what it is.

If two triangles are similar, their corresponding sides are proportional.
. . (This means they have the same ratio.)

            *
           *  *
          *     *                   *
      25 *        *                *  *
        *           *          10 *     *
       *              *          *        *
      *  *  *  *  *  *  *       *  *  *  *  *
              32                      x

\(\displaystyle \text{In the small triangle, the ratio of the base to the left side is }\tfrac{x}{10}\)

\(\displaystyle \text{In the large triangle, the ratio of the base to the left side is }\tfrac{32}{25}\)

\(\displaystyle \text{Since these ratios are equal, we have: }\:\frac{x}{10} \,=\,\frac{32}{25}\)

\(\displaystyle \text{Now solve for }x.\)