The base of a right triangle. is 48 cm and its hypotenuse is 50 cm long.

Question:

The base of a right triangle. is 48 cm and its hypotenuse is 50 cm long. The area of the triangle is
(a) 168 cm2
(b) 252 cm2
(c) 336 cm2
(d) 504
 cm2

Solution:

(c) 336 cm2

Let $\triangle P Q R$ be a right-angled triangle and $\mathrm{PQ} \perp \mathrm{QR}$.

Now,

$P Q=\sqrt{P R^{2}-Q R^{2}}$

$=\sqrt{50^{2}-48^{2}}$

$=\sqrt{2500-2304}$

$=\sqrt{196}$

 

$=14 \mathrm{~cm}$

$\therefore$ Area of triangle $=\frac{1}{2} \times Q R \times P Q=\frac{1}{2} \times 48 \times 14=336 \mathrm{~cm}^{2}$

 

 

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