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A square and an equilateral triangle have the same perimeter. Each side of the triangle is 16 m. How do you find the length of each side of the square?

1 Answer

Jan 27, 2016

#"Side"_square = 8root(4)(3)#

Explanation:

The semi-perimeter of the equilateral triangle is
#color(white)("XXX")s=(16+16+16)/2 = 24#

So, by Heron's formula
#color(white)("XXX")"Area"_triangle = sqrt(24xx8xx8xx8) =8^2sqrt(3)#

We are told #"Area"_square = "Area"_triangle#

So #Area"_square = 8^2sqrt(3)#

and each side of the square has a length of
#color(white)("XXX")sqrt(8^2sqrt(3)) = 8root(4)(3)#

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