Question

Triangles ABC and DEF are similar.
If area (ΔABC) = 9 cm², area (ΔDEF) = 64 cm² and DE = 5.1 cm, find AB.

Answer 1

We have
area (Δ ABC) = 9 cm²
area (Δ DEF) = 64 cm²
and DE = 5.1 cm
Since, `"area (Δ ABC)"/"area (Δ DEF)" = "AB"^2/"DE"^2`
⇒ `(9)/(64) = "AB"^2/"DE"^2`
⇒ `"AB"/"DE" = (3)/(8)`
⇒ `"AB"/(5.1) = (3)/(8)`
⇒ AB = `(3)/(8) xx 5.1 = (15.3)/(8)`
⇒ AB = 1.9125 cm.