SSC Sample Paper Mock Test-8 SSC CGL Tear-II Paper-1

\[\Delta ABC\] is such that AB = 3 cm, BC = 2 cm and AC = 2.5 cm. A DBF is similar to A ABC. If EF = 4 cm, then the perimeter of A DEF is

A) 5 cm

B) 7.5 cm

C) 15 cm

D) 18 cm

Correct Answer: C

Solution :

As \[\Delta ABC\sim \Delta DEF\]\[\Rightarrow \]\[\frac{AB}{DE}=\frac{AC}{DF}=\frac{BC}{EF}\]

\[\Rightarrow \] But \[\frac{BC}{EF}=\frac{2}{4}=\frac{1}{2}\]

\[\therefore \] \[DE=2AB=2\times 3=6\,\,\text{cm}\]

\[DF=2\times AC=2\times 2.5=5\,\,\text{cm}\]

\[\therefore \]Perimeter of \[\Delta DEF=(6+5+4)=15\,\,\text{cm}\]

Shortcut method

\[\frac{\text{Perimeter}\,\,\text{of}\,\,\Delta ABC}{\text{Perimeter}\,\,\text{of}\,\,\Delta DEF}=\]Ratio of corresponding sides

\[\therefore \] \[\frac{(3+2+2.5)}{\text{Perimeter}\,\,\text{of}\,\,\Delta DEF}=\frac{1}{2}\]

\[\therefore \] Perimeter of \[\Delta DEF=2\,\,(7.5)=15\,\,\text{cm}\]