Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
A square and an equilateral triangle have equal perimeters. If the diagonal of the square is $12 \sqrt{2} \mathrm{cm}$, then the area of the triangle is
(a)$24 \sqrt{2} \mathrm{cm}^{2}$
(b)$24 \sqrt{3} \mathrm{cm}^{2}$
(c)$48 \sqrt{3} \mathrm{cm}^{2}$
(d)$64 \sqrt{3} \mathrm{cm}^{2}$
Answer
Answer (as printed): D
Explanation
Let the side of the square be $a$ cm. Then, its diagonal $=\sqrt{2} a \mathrm{cm}$. Now, $\sqrt{2} a=12 \sqrt{2} \Rightarrow a=12 \mathrm{cm}$. Perimeter of the square $=4 a=48 \mathrm{cm}$. Perimeter of the equilateral triangle = 48 cm. Each side of the triangle = 16 cm. Area of the triangle $=\left(\frac{\sqrt{3}}{4} \times 16 \times 16\right) \mathrm{cm}^{2}=(64 \sqrt{3}) \mathrm{cm}^{2}$.