Subject: General Aptitude · Chapter: Area · Exam: 2004 · Marks: · Difficulty:
The area of a triangle is $216 \mathrm{cm}^{2}$ and its sides are in the ratio 3 : 4 : 5. The perimeter of the triangle is
(a)6 cm
(b)12 cm
(c)36 cm
(d)72 cm
Answer
Answer (as printed): D
Explanation
Let $a=3 x \mathrm{cm}, b=4 x \mathrm{cm}$ and $c=5 x \mathrm{cm}$. Then, $s=6 x \mathrm{cm}$. $$\begin{aligned} A & =\sqrt{s(s-a)(s-b)(s-c)} \\ & =\sqrt{6 x \times 3 x \times 2 x \times x}=\left(6 x^{2}\right) \mathrm{cm}^{2} . \\ \therefore 6 & x^{2}=216 \Leftrightarrow x^{2}=36 \Leftrightarrow x=6 . \end{aligned}$$ So $a=18 \mathrm{cm}, b=24 \mathrm{cm}$ and $c=30 \mathrm{cm}$. Perimeter $=(18+24+30) \mathrm{cm}=72 \mathrm{cm}$.