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Answer:
8.5 cm
Step-by-step explanation:
We know that the square has side lengths of 6cm. To calculate the distance from one corner of the square to the opposite corner, we are calculating the diagonal of the square.
Along the diagonal is where the square gets split in half into two right triangles. The Pythagorean theorem states that [tex]a^2+b^2=c^2[/tex] where c is the longest side of a right triangle and a and b are the other two sides.
To find the length of the square's diagonal, we essentially need to calculate c, the longest side of the triangles. We can do this by plugging 6 into the equation as a and b.
[tex]a^2+b^2=c^2\\6^2+6^2=c^2\\36+36=c^2\\72=c^2\\\sqrt{72} =c[/tex]
[tex]8.5[/tex] ≈ [tex]c[/tex]
Therefore, it will be approximately 8.5cm from one corner of the square to the opposite corner.
I hope this helps!