The length of the diagonal of a squere is 36 feet. Find the length of the side of the square.

Length of the side of a square is 18 sqrt(2)

Step-by-step explanation:

a and b are the sides of square and c is the diagonal.

a^2+b^2=c^2

a^2+b^2= 36^2

As all sides are equal we can take b=a

2a^2=36^2

a^2= (36×36)/2

a^2 = 18×36 = 2×9×9×4

Taking squareroot on both sides we get

a= sqrt(2×9×9×2×2)

a=18 sqrt(2)

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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step-by-step explanation: