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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