Question

Find the ratio of area of the equilateral triangles whose sides are 3 and 4 units.

• A. 9 : 25
• B. 9: 16
• C. 16: 25
• D. None of the above

Answer 1

The correct option is B

9: 16

Let the triangles be $△ABC$ and $△DEF$

Then $AB=3$ units and $DE=4$ units.

Each angle of both $△ABC$ and $△DEF$ is ${60}^{\circ }$.

$△ABE\sim △$ ACF
( AAA similarity)

So,
$\frac{ar\left(ABC\right)}{ar\left(DEF\right)}=\frac{B{C}^2}{E{F}^2}=\frac{3^2}{4^2}=\frac{9}{16}$