Similar Triangles (Easy)

AMC 10 Q1–8 depth — contest entry, not school drills.

Similar Triangles: core idea

AA recognition.

Similar triangles have side ratio $2:3$ . If the smaller matching side is $8$ , find the larger side.

Hint: Match corresponding sides and use one scale factor. Answer: 12.

1. A $3$ -foot pole casts a $4$ -foot shadow. A tree casts a $20$ -foot shadow. Find the tree height.
2. In similar triangles, $AB=6$ , $DE=10$ , and $EF=15$ correspond. Find $BC$ .
3. A triangle similar to a $5$ - $12$ - $13$ triangle has hypotenuse $26$ . Find its shortest side.
4. Two similar triangles have perimeters $18$ and $30$ . A side of the first is $6$ . Find its corresponding side.
5. A $9$ by $12$ rectangle is enlarged so its shorter side is $15$ . Find the new longer side.
6. Triangles $ABC$ and $DEF$ are similar. If $AB/DE=4/7$ and $AC=16$ , find $DF$ .
7. A map scale is $1:50000$ . A road measures $3$ cm on the map. How many meters is the real road?
8. A $6$ - $8$ - $10$ triangle is reduced so its hypotenuse is $5$ . Find its area.
9. Two similar figures have area ratio $49:81$ . Find their side-length ratio, smaller to larger.