Find the ratio of area of the equilateral triangles whose sides are 3 and 4 units. Options: A . &nbsp 9 : 25 B . &nbsp 9: 16 C . &nbsp 16: 25 D . &nbsp None of the above

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

Question

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

Options:

A . 9 : 25

B . 9: 16

C . 16: 25

D . None of the above

Answer: Option B
:
B

Let the triangles be $△ A B C$ and $△ D E F$
Then $A B = 3$ units and $D E = 4$ units.

Each angle of both $△ A B C$ and $△ D E F$ is $60^{\circ}$ .

$△ A B E \sim △$ ACF
( AAA similarity)

So,
$\frac{a r (A B C)}{a r (D E F)} = \frac{B C^{2}}{E F^{2}} = \frac{3^{2}}{4^{2}} = \frac{9}{16}$

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