Question

If triangle ABC ~ triangle DEF, BC=6 cm. EF=8 cm, find the ratio of triangle ABC to triangle DEF

Answer 1

As we know, that ratio of the areas of 2 similar triangles = the ratio of the squares of their corresponding sides.


so
area ABC:areaDEF=BC^2:EF^2
=6^2:8^2
=36:64
=9:16

Answer 2

$\underline{\bold{Given:-}}$

∆ABC ~ ∆DEF

BC = 6 cm

EF = 8 cm

$\underline{\bold{To\:find:-}}$

Ratio area of triangle ABC and DEF

$\underline{\bold{Solution:-}}$

Since, ∆ABC ~ ∆DEF

So,

$\bold{The \: ratio \: of \: the \: areas \: of \: two} \\\bold{similar \: triangles \: is \: equal \: to }\\ \bold{the \: square \: of \: the \: ratio \: of \: their} \\\bold{ corresponding \: sides.} \\ \\ \frac{Area \: of \: triangle \: ABC}{Area \: of \: triangle \:EF } = \frac{ {BC}^{2} }{ {EDF}^{2} } \\ \\ = \frac{ {6}^{2} }{ {8}^{2} } \\ \\ = \frac{36}{64} \\ \\ = \frac{9}{16}$