Question

Triangles ABC and DEF are similar.
If area (ΔABC) = 16 cm², area (ΔDEF) = 25 cm² and BC = 2·3 cm find EF.

Answer 1

We have
area (ΔABC) = 16 cm²
area (ΔDEF) = 25 cm²
and BC = 2·3 cm
Since , ${\displaystyle \frac{\text{area (ΔABC)}}{\text{area (ΔDEF)}}=\frac{{\text{BC}}^2}{{\text{EF}}^2}}$
⇒ ${\displaystyle \frac{16}{25}=\frac{{\left(2.3\right)}^2}{{\text{EF}}^2}}$
⇒ ${\displaystyle \frac{2·3}{\text{EF}}=\frac{4}{5}}$
⇒ 4EF = 5 x 2·3
⇒ EF = ${\displaystyle \frac{11.5}{4}}$
⇒ EF = 2·875 cm.