Subject: General Aptitude · Chapter: Area · Exam: 2007 · Marks: · Difficulty:
The areas of two equilateral triangles are in the ratio 25 : 36. Their altitudes will be in the ratio
(a)25 : 36
(b)36 : 25
(c)5 : 6
(d)$\sqrt{5}: \sqrt{6}$
Answer
Answer (as printed): C
Explanation
Let the length of sides of the two triangles be $a_{1}$ and $a_{2}$ respectively and their altitudes be $h_{1}$ and $h_{2}$ respectively. Then, $$\frac{\frac{\sqrt{3}}{4} a_{1}^{2}}{\frac{\sqrt{3}}{4} a_{2}^{2}}=\frac{25}{36} \Rightarrow\left(\frac{a_{1}}{a_{2}}\right)^{2}=\left(\frac{5}{6}\right)^{2} \Rightarrow \frac{a_{1}}{a_{2}}=\frac{5}{6} .$$
Explanation as extracted from the printed page; notation may be imperfect.