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cdw2014
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.





The diagonals of a square measure 14cm. therefore, the length of a side of the square is 7√2cm.

How are the sides of a square and its diagonals are related?

Since a square has its adjacent sides perpendicular to each other, thus, drawing a diagonal gives us two right-angled triangles, both congruent. Assuming that the length of the sides of a square = a units, then,

by using the Pythagoras theorem, we get the length of its diagonal as:

[tex]D^2 = a^2 + a^2\\\\D = \sqrt{2a^2} = a\sqrt{2} \: \rm units[/tex]

The sides of a square have the same lengths, so the diagonal and two sides form a 45-45-90 right triangle.

Therefore, the sides of the square would be

[tex]D = a\sqrt{2} \: \rm units\\\\14 = a\sqrt{2}[/tex]

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

a = 7√2

Thus, the answer is A.

Learn more about square;

https://brainly.com/question/1658516

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