question_answer

\[\Delta ABC\tilde{\ }\Delta DEF\]. If \[AB=4cm,\] \[\text{BC}=\text{3}\text{.5 cm},\] \[\text{CA}=\text{2}\text{.5 cm}\]and \[\text{DF}=\text{7}\text{.5 cm},\]the perimeter of \[\Delta DEF\] is:                     (CBSE 2017)

A) 20 cm

B) 30 cm

C) 35 cm

D) 47 cm

Correct Answer: B

Solution :

[b] Given, \[\Delta ABC-\Delta DEF\]

\[\therefore \,\,\,\,\,\,\,\,\frac{\text{Perimeter of}\,\,\Delta \text{ABC}}{\text{Perimeter of}\,\,\Delta \text{DEF}}=\frac{AC}{DE}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\frac{AB+BC+AC}{\text{Perimeter of}\,\,\Delta \text{DEF}}=\frac{AC}{DF}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\frac{4+3.5+2.5}{\text{Perimeter of}\,\,\Delta \text{DEF}}=\frac{2.5}{7.5}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\frac{10}{\text{Perimeter of}\,\,\Delta \text{DEF}}=\frac{1}{3}\]

\[\Rightarrow \]     Perimeter of \[\Delta DEF=3\times 10=30\]

Hence, perimeter of \[\Delta DEF\] is 30 cm.