Question

let ∆ABC ∆DEF and their areas be, respectively, 81cm^2 and 121cm^2 . if EF = 15.4cm find BC​

Answer 1

Answer:

Okay, we know that if two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides. So:

$\frac{ar(\triangle ABC)}{ar(\triangle DE\:F)}=\frac{AB^{2} }{DE^{2} } =\frac{BC^{2} }{EF^{2} } =\frac{AC^{2} }{DF^{2} }$

Only consider $\frac{ar(\triangle ABC)}{ar(\triangle DE\:F)}=\frac{BC^{2} }{EF^{2} }$ because the question only involves the sides EF and BC. Now, substitute the values.

$\frac{81}{121}=\frac{BC^{2} }{15.4^{2} }$

$\frac{81\times15.4^{2} }{121}=BC^{2}$

$\frac{19209.96}{121} =BC^{2}$

$BC=\sqrt{158.76}$

$BC=12.6 \: cm.$

THUS, BC IS 12.6 cm.

HOPE THIS HELPS :D