Thread: 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!

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 is:.
. . We have:.

The area of an equilateral triangle of side is:.
. . We have:.

Therefore: .

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