# Thread: Percentages and more percentages!

1. ## Percentages and more percentages!

Hi again. I am back after posting my first post which was two minutes ago. I have a question. "A square and an equilateral triangle have sides that are equal at 42.61 feet. What percentage of the squares area is the area of the triangle?" Thank you again!

2. ## Re: Percentages and more percentages!

Hello, evilgummybear!

A square and an equilateral triangle have sides that are equal at 42.61 feet.
What percentage of the square's area is the area of the triangle?

The area of a square of side $\displaystyle x$ is:.$\displaystyle A_S \,=\,s^2$
. . We have:.$\displaystyle A_S \:=\:42.61^2 \:=\:1815.6121\text{ ft}^2.$

The area of an equilateral triangle of side $\displaystyle s$ is:.$\displaystyle A_T \:=\:\tfrac{\sqrt{3}}{4}x^2$
. . We have:.$\displaystyle A_T \:=\:\tfrac{\sqrt{3}}{4}(42.61)^2 \:=\:786.183101$

Therefore: .$\displaystyle \frac{A_T}{A_S} \;=\;\frac{786.183101}{1815.6121} \;=\;0.433012702 \;\approx\;43.3\%$

3. ## Re: Percentages and more percentages!

In fact you need not find the area at all. Just use the expressions for area and you will get the same result irrespective of the length of the side.
AT = √3/4 〖side 〗^2 and AS = 〖side 〗^2
A_T/A_s = ( √3/4 〖side 〗^2)/〖side 〗^2 =√3/4 ≈0.4330127018922193