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  • If \Delta ABC \sim \Delta DEF, AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, {find the perimeter of }\Delta ABC.

If \\ \Delta ABC \sim \Delta DEF, AB = 4 cm, DE = 6 cm, EF = 9 cm \; and \; FD = 12 cm, find the perimeter of \Delta ABC.

Answers (1)

Answer: 18 cm

Given : \Delta ABC \sim \Delta DEF

and      AB = 4cm , DE = 6 cm

           EF = 9 cm, FD = 12 cm

Here \Delta ABC \sim \Delta DEF   (given)

\therefore \frac{AB}{ED}=\frac{BC}{EF}=\frac{AC}{DF}

       \frac{4}{6}=\frac{BC}{9}=\frac{AC}{12}

Taking first two terms we get

\frac{4}{6}=\frac{BC}{9}

\frac{9 \times 4}{6}=BC

BC=6 \; cm

Taking first and last terms we get

\frac{4}{6}=\frac{AC}{12}

AC=\frac{4 \times 12}{6}=8

Perimeter \; of\; \Delta ABC = AB + BC + CA

                                                 = 4 + 6 + 8 = 18 \; cm.

Posted by

infoexpert23

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