Question

The area of two equilateral triangles are in the ratio 25 : 36. Their altitudes will be in the ratio :

• A. 25 : 36
• B. 36 : 25
• C. \sqrt{5}$ : $\sqrt{6}
• D. 5 : 6

Answer 1

Answer:

D. 5 : 6

Let the length of sides of the two triangles be a1 and a2 respectively and their altitudes be h1 and h2 respectively.

Then, ⇔$\frac{\frac{\sqrt{3}}{4}a1^2}{\frac{\sqrt{3}}{4}a2^2}=\frac{25}{36}$

$\frac{a1^2}{a2^2}=\frac{25}{36}$

$\frac{a1}{a2}=\frac{5}{6}$

and.,

$\frac{\frac{1}{2}\times{a1}\times{h1}}{\frac{1}{2}\times{a1}\times{h1}}=\frac{25}{36}$

$\frac{5h1}{6h2}=\frac{25}{36}$

$\frac{h1}{h2}=\frac{5}{6}$

AltitudeRatio h1: h2 = 5 : 6