ΔABC be a right-angled triangle where ∠A = 90° and AD ⊥ BC. If ar (ΔABC) = 40 cm², ar (ΔACD) = 10 cm² and AC = 9 cm, then the length of BC is

Solution(By Examveda Team)

According to question,
Given: AC = 9 cm

area of ΔABC = 40 cm²
area of ΔADC = 10 cm²
ΔABC ∼ ΔADC


$$\frac{{{\text{area}}\,{\text{of}}\,\Delta ABC}}{{{\text{area}}\,{\text{of}}\,\Delta ADC}} = \frac{{A{B^2}}}{{A{D^2}}} = \frac{{B{C^2}}}{{A{C^2}}}$$
(In similar Δratio of their area is square of ratio of corresponding sides)
$$\eqalign{ & \frac{{40}}{{10}} = \frac{{B{C^2}}}{{{{\left( 9 \right)}^2}}} \cr & \frac{{40}}{{10}} \times 81 = B{C^2} \cr & BC = 18\,{\text{cm}} \cr} $$