Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
The perimeter of a right-angled triangle is 60 cm. Its hypotenuse is 26 cm. The area of the triangle is
(a)$120 \mathrm{cm}^{2}$
(b)$240 \mathrm{cm}^{2}$
(c)$390 \mathrm{cm}^{2}$
(d)$780 \mathrm{cm}^{2}$
Answer
Answer (as printed): A
Explanation
Let Base $=b \mathrm{cm}$ and Height $=h \mathrm{cm}$. $$b+h+26=60 \Leftrightarrow b+h=34 \Leftrightarrow(b+h)^{2}=(34)^{2}$$ $\therefore(b+h)^{2}-\left(b^{2}+h^{2}\right)=(34)^{2}-(26)^{2}$ $\Leftrightarrow 2 b h=(34+26)(34-26)=480$ $\Leftrightarrow b h=240 \Leftrightarrow \frac{1}{2} b h=120$. ∴ Area $=120 \mathrm{cm}^{2}$.