The length of the sides of the rectangle is 6 and 8. Through the point O of the intersection of the diagonals

| June 25, 2021 | education

The length of the sides of the rectangle is 6 and 8. Through the point O of the intersection of the diagonals of the rectangle, a straight line OK is drawn, perpendicular to its plane. Find the distance from point K to the vertices of the rectangle if OK = 12.

In a right-angled triangle ACD, according to the Pythagorean theorem, we determine the length of the hypotenuse AC.

AC ^ 2 = AD ^ 2 + CD ^ 2 = 64 + 36 = 100. AC = 10 cm.

Since ABCD is a rectangle, its diagonals are equal and are halved at point O.

ОА = ОВ = ОВ = ОD = АС / 2 = 5 cm.

Since the lengths of the halves of the diagonals are equal, the distance from point K to the vertices of the rectangle will be the same. In a right-angled triangle OAK, by the Pythagorean theorem, we determine the length of the hypotenuse AK.

AK ^ 2 = AO ^ 2 + OK ^ 2 = 25 + 144 = 169.

AK = 13 cm.

Answer: From point K to the vertices of the rectangle 13 cm.



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