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A square and an equilateral triangle have equal perimeters. The area of the triangle is 8 sqrt 3 square inches. What is the number of inches in the length of the diagonal of the square?

 Nov 7, 2020
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find side length of triangle

1/2 b h = 8 sqrt3

bh = 16 sqrt3

b  * b sin60 = 16 sqrt3

b^2  sqrt3/2 = 16 sqrt 3

b^2 = 32

b = sqrt 32

 

so perimeter is   3 sqrt 32      square side is then  3/4 sqrt 32  

    diagonal^2  is     2 (3/4 sqrt32)^2  = 18/16 *32              d = 6 in

 Nov 7, 2020

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