The length of the diagonal of a square is 8 cm. How long are the sides of the square?
February 20th, 2023
The sides are ##4sqrt2## cm long
Pythagorus tells us that for any right triangle, ##a^2 + b^2 = c^2## where c is the hypotenuse.
A square can be divided into two right triangles along its diagonal, and these triangles are isosceles such that ##a=b##, as all sides of a square are equal.
So we can say that ##a^2+a^2=8^2##, or
##2a^2=64##
##a^2 = 32##
##a=sqrt32=4sqrt2##
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The length of the diagonal of a square is 8 cm. How long are the sides of the square?
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