Question

The perimeters of two similar triangles are $30cm$ and $20cm$ respectively. If one side of the first triangle is $12cm$, determine the corresponding side of the second triangle.

Answer 1

Hint: Here we will apply the property of similar triangles i.e., “Ratio of corresponding sides of similar triangles is equal to the ratio of their perimeters” to determine the corresponding side of the second triangle.

Complete step-by-step answer:

According to the given data, let us consider
$\Delta ABC$ as the first triangle with the perimeter ${P_1}$.
$\Delta DEF$ as the second triangle with the perimeter ${P_2}$.
Here the triangles $\Delta ABC$ and $\Delta DEF$ are similar triangles.

Given that,
One side of the first triangle is$12cm$, which means $AB = 12cm$($\because $ $\Delta ABC$ is the first triangle).
$
  {P_1} = 30cm \\
  {P_2} = 20cm \\
 $
Since the triangles given are similar triangles.
We know that “Ratio of corresponding sides of similar triangles is equal to the ratio of their perimeters”.
By using the above condition we can write
$ \Rightarrow \dfrac{{AB}}{{DE}} = \dfrac{{BC}}{{EF}} = \dfrac{{AC}}{{DE}} = \dfrac{{{P_1}}}{{{P_2}}}$
Therefore we can write it as
$\dfrac{{AB}}{{DE}} = \dfrac{{{P_1}}}{{{P_2}}}$
By substituting the values in the above condition, we get
$ \Rightarrow \dfrac{{12}}{{DE}} = \dfrac{{30}}{{20}}$
$ \Rightarrow DE = \dfrac{{12 \times 20}}{{30}}$
$ \Rightarrow DE = 8cm$
Hence from this we can say that the length of the corresponding side of the second triangle = $8cm$.

Note: After applying the similar triangle property of perimeter, we have to take the required condition which has values. Avoid unnecessary conditions and calculations.