question_answer

If the perimeters of two similar triangles ABC and DEF are 50 cm and 70 cm respectively and one side of\[\Delta \,ABC=20\text{ }cm\], then find the corresponding side of \[\Delta \,DEF\].

Answer:

Given,               \[\Delta \,ABC\sim \Delta \,DEF,\]

Perimeter of \[\Delta \,ABC=50\,cm\]

Perimeter \[\Delta \,DEF=70\,\,cm\]

One side of \[\Delta \,ABC=20\text{ }cm\]

Let                    \[AB=20\text{ }cm\]

\[\Delta \,ABC\sim \Delta \,DEF\]                  [Given]

\[\therefore \frac{\text{Peri}\,(\Delta \,ABC)}{\text{Peri}\,(\Delta \,DEF)}=\frac{AB}{DE}\]

\[\frac{50}{70}=\frac{20}{DE}\]

\[\Rightarrow 5DE=140\]

\[DE=28\,\,m\]

The corresponding side of \[\Delta \,DEF=28\text{ }cm\].