Question

A square has the same area as an equilateral triangle. What is the ratio of the perimeter of the equilateral triangle to the perimeter of the square?

Answer 1

Area of Equilateral Triangle is how much can you tell??

Answer 2

Do you know I am asking you??

Answer 3

A Square with side a has Area = \(s^2\)

Area of Equilateral Triangle = \(\frac{\sqrt{3}}{4} \times a^2\)

Answer 4

Then I think you know the answer too..

Answer 5

I got 3^.25a : 2s, but the answer is 3^.75a : 2s

Answer 6

\[\large s^2 = \frac{\sqrt{3}}{4} \times a^2 \implies s = \frac{(3)^{\frac{1}{4}}a}{4}\]

Answer 7

You forgot the square root of 4.

Answer 8

Now take the ratio:

\[\frac{3a}{4s} \implies \frac{3 \times 2}{4 \cdot (3)^{\frac{1}{4}}}\]

Solve this..

Answer 9

\[\sqrt[4]{3} = (3)^{\frac{1}{4}}\]

Answer 10

3^.75/2

Answer 11

That is the ratio..

Answer 12

Why are you taking s and a there?? They will be cancel out on substitution..

Answer 13

*get cancelled..

Answer 14

I'm still confused.

Answer 15

Yeah that is 2 instead of 4.. My mistake there..

Answer 16

Where??

You can freely tell me..

Answer 17

Got ??

Answer 18

Yes.

Answer 19

Good..