Question

Triangles ABC and DEF are similar. Find the
perimeter of triangle DEF.
a. 34.7 cm
b. 25.3 cm
c. 15 cm
d. 38 cm
Please show work to help me understand.

Answer 1

If Both triangles are similar the ratio of sides will be same

$\\ \sf\longmapsto \dfrac{AB}{AC}=\dfrac{DE}{DF}$

$\\ \sf\longmapsto \dfrac{8}{10}=\dfrac{12}{DF}$

$\\ \sf\longmapsto 8DF=120$

$\\ \sf\longmapsto DF=\dfrac{120}{8}$

$\\ \sf\longmapsto DF=15cm$

Now

$\\ \sf\longmapsto Perimeter=DF+DE+EF$

$\\ \sf\longmapsto Perimeter=15+11+12$

$\\ \sf\longmapsto Perimeter=38cm$