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

Answer: Option B

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)
$$\begin{array}{rl}& \frac{40}{10}=\frac{B{C}^2}{{\left(9\right)}^2}\\ & \frac{40}{10}\times 81=B{C}^2\\ & BC=18\text{cm}\end{array}$$