In two triangles, ∆ABC ∼ ∆PQR, AB=12cm and PQ=4cm, if AL and PM are altitudes of the respected triangles, then what will be AL : PM?
Key Property of Similar Triangles
For two similar triangles, the ratio of their corresponding altitudes is equal to the ratio of their corresponding sides.
Given that ∆ABC ∼ ∆PQR:
- The corresponding sides are AB and PQ.
- The corresponding altitudes are AL and PM.
Calculating Altitude Ratio
According to the property of similar triangles:
\( \frac{AL}{PM} = \frac{AB}{PQ} \)
Substituting Given Values
We are given:
- AB = 12cm
- PQ = 4cm
Substitute these values into the equation:
\( \frac{AL}{PM} = \frac{12cm}{4cm} \)
Finding the Ratio
Simplify the fraction:
\( \frac{AL}{PM} = 3 \)
Therefore, the ratio AL : PM is 3:1.
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