Question : Find the area of a right-angled triangle whose base is 12 cm and the hypotenuse is 13 cm.
Option 1: 30 cm2
Option 2: 55 cm2
Option 3: 65 cm2
Option 4: 22 cm2
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Correct Answer: 30 cm 2
Solution :
Area of right-angled triangle $=\frac{1}{2}\times \text{Base}\times\text{Height}$
Given, Base = 12 cm and Hypotenuse = 13 cm
Let the perpendicular be $p$.
Using Pythagoras theorem,
$\small\text{Hypotenuse}^2=\text{Base}^2+\text{Perpendicular}^2$
⇒ $13^2=12^2+p^2$
⇒ $169=144+p^2$
⇒ $p^2=25$
⇒ $p=5$ cm
$\therefore$ Area $= \frac{1}{2}\times 12\times 5=6\times 5 = 30$ cm$^2$
Hence, the correct answer is 30 cm$^2$.
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