Question : Suppose $\triangle A B C$ be a right-angled triangle where $\angle A=90^{\circ}$ and $A D \perp B C$. If area $(\triangle A B C)$ $=80 \mathrm{~cm}^2$ and $BC=16$ cm, then the length of $AD$ is:
Option 1: 10 cm
Option 2: 24 cm
Option 3: 18 cm
Option 4: 12 cm
Correct Answer: 10 cm
Solution :
Base, BC = 16 cm
Area $(\triangle A B C)$ $=80 \mathrm{~cm}^2$
$A D \perp B C$
Area of $(\triangle A B C)$ = $\frac{1}{2}\times BC \times AD$
⇒ 80 = $\frac{1}{2}\times 16 \times AD$
⇒ AD = 10 cm
Hence, the correct answer is 10 cm.
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