Subject: General Aptitude · Chapter: Area · Exam: 2003 · Marks: · Difficulty:
If an equilateral triangle of area $X$ and a square of area $Y$ have the same perimeter, then $X$ is
(a)equal to $Y$
(b)greater than $Y$
(c)less than $Y$
(d)less than or equal to $Y$
Answer
Answer (as printed): C
Explanation
Let each side of the triangle be $a \mathrm{cm}$ and each side of the square be $b$ cm. Then, $\mathrm{X}=\frac{\sqrt{3}}{4} a^{2}$ and $\mathrm{Y}=b^{2}$, where $3 a=4 b$, i.e., $b=\frac{3 a}{4}$. $$\therefore \quad \mathrm{X}=\frac{\sqrt{3}}{4} a^{2} \text { and } \mathrm{Y}=\frac{9 a^{2}}{16} \quad\left[\because b=\frac{3 a}{4}\right]$$ Now, $\frac{\sqrt{3}}{4} a^{2}=\frac{1.732}{4} a^{2}=0.433 a^{2}$ and $\frac{9 a^{2}}{16}=0.5625 a^{2}$. $$\therefore \quad X<Y .$$