# Percentages and more percentages!

• Feb 16th 2013, 04:23 PM
evilgummybear
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!
• Feb 16th 2013, 07:33 PM
Soroban
Re: Percentages and more percentages!
Hello, evilgummybear!

Quote:

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: .$\displaystyle \frac{A_T}{A_S} \;=\;\frac{786.183101}{1815.6121} \;=\;0.433012702 \;\approx\;43.3\%$
• Feb 16th 2013, 09:26 PM
ibdutt
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
Attachment 27074