The length of the side of the rectangle ABCD is 8 cm and 6 cm through the point O of intersection of its diagonal

| March 2, 2021 | education

The length of the side of the rectangle ABCD is 8 cm and 6 cm through the point O of intersection of its diagonal a straight line OK is drawn, perpendicular to its plane. Find the distance from point K to the top of the rectangle if OK is 12 cm.

1. It is known that the diagonals of a rectangle are equal and are halved at the point of intersection.

2. So the triangle OВС is isosceles, and the OВ side is equal to the OС side.

3. The perpendicular OE, lowered from point O to the side BC, divides the side in half, and then

BE = EC = BC: 2 = 8: 2 = 4 cm.

4. The height OE is equal to 1/2 of the side AB, because the triangle OBC is equal to the triangle AOD (according to the first sign of equality of triangles).

OE = 1/2 AB = 6: 2 = 3 cm.

5. By the Pythagorean theorem, we define the side of the OS of the triangle OEC.

OC = (OE ^ 2 + EC ^ 2) ^ 1/2 = (3 ^ 2 + 4 ^ 2) ^ 1/2 = (9 + 16) ^ 1/2 = 5 cm.

6. From the right-angled triangle KС we find the side of KС using the Pythagorean theorem.

KС = (OС ^ 2 + OK ^ 2) ^ 1/2 = (5 ^ 2 + 12 ^ 2) ^ 1/2 = (25 + 144) ^ 1/2 = 169 ^ 1/2 = 13.

7. Distances from point K to all vertices of the rectangle are the same and equal to the length of the COP 13 cm.

Answer: The distance from point K to the vertices of the rectangle is 13 cm.



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