the diagonals of a square measure 14cm. Which is the length of a side of the square?

The sides of a square have the same lengths, so the diagonal and two sides form a 45-45-90 right triangle. In a 45-45-90 triangle, the hypotenuse has a length with is [tex] \sqrt{2} [/tex] longer than the legs.

Therefore, the sides of the square would be [tex] \frac{14}{ \sqrt{2} } [/tex].

Rationalize the fraction be multiplying the numerator and denominator by root 2.

[tex] \frac{14 \sqrt{2} }{2} [/tex]

The 14 and 2 will reduce to 7, and the answer is A.