Ratio of the area of a square to the area of a triangle  TOPIC_SOLVED

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Ratio of the area of a square to the area of a triangle

Postby kevin on Thu Jul 07, 2011 6:02 am

What is the ratio of the area of a square of side 5 to an equilateral triangle with sides of 5? Doesn't seem like a hard question, but the given answer is 4sqrt(3)/3.

Any ideas on how to get to this final answer?


Thanks
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Re: Ratio of the area of a square to the area of a triangle

Postby little_dragon on Thu Jul 07, 2011 2:57 pm

kevin wrote:What is the ratio of the area of a square of side 5 to an equilateral triangle with sides of 5? Doesn't seem like a hard question, but the given answer is 4sqrt(3)/3.

wat areas did U get? wat did U get when U divided?
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Re: Ratio of the area of a square to the area of a triangle

Postby kevin on Thu Jul 07, 2011 5:03 pm

I got 25 for the area of the square and the triangle I got 6.25
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Re: Ratio of the area of a square to the area of a triangle

Postby maggiemagnet on Thu Jul 07, 2011 5:53 pm

kevin wrote:I got 25 for the area of the square and the triangle I got 6.25

You shouldn't have gotten an exact decimal value for the triangle, so something went wrong there. Please reply showing your steps, starting with finding the altitude of the equilateral triangle (possibly using the ratios for a 30-60-90 triangle, which is half of an equilateral). Thanks!

:clap:
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Re: Ratio of the area of a square to the area of a triangle  TOPIC_SOLVED

Postby monkeyolsen on Sat Jul 09, 2011 4:24 pm

area of square = 5*5 = 25

Triangle

altitude:
let the altitude of the equilateral triangle be x
5^2 = (2.5)^2 + x^2
x^2 = 25-(25/4)
= 75/4
x = 5root(3)/2

area of triangle = (b*h)/2
b = 5
h= x = 5root(3)/2

area = [(5)*(5root(3)/2)]/2
= 25root(3)/4

ratio of area of square to area of triangle = 25/[25root(3)/4]
= [25*4]/[25 root(3)] = 4/[root(3)]

multiply top and bottom by [root(3)]
4*root(3)/[root(3)*root(3)] = 4root(3)/3
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