The point in space is 40 cm away from all the vertices of the square, the second point is 25 cm away from this point

| September 3, 2021 | education

The point in space is 40 cm away from all the vertices of the square, the second point is 25 cm away from this point and from the vertices of the square. Find the area of the square.

Triangles AOK and AOM are rectangular with a common leg AO.

Let the length of the segment OK = X cm, then the length of the segment OM = (25 + X) cm.

From two triangles, according to the Pythagorean theorem, we express the leg AO.

AO ^ 2 = AK ^ 2 – OK ^ 2 = 625 – X2.

AO ^ 2 = AM ^ 2 – OM ^ 2 = 1600 – 625 – 50 * X – X ^ 2.

625 – X ^ 2 = 1600 – 625 – 50 * X – X ^ 2.

50 * X = 350.

X = 7 cm.

Then AO ^ 2 = AK ^ 2 – OK ^ 2 = 625 – 49 = 576.

AO = 24 cm.

Then AC = 2 * 24 = 48 cm.

Let’s define the area of the square.

Savsd = AC ^ 2/2 = 48 ^ 2/2 = 1152 cm2.

Answer: The area of the square is 1152 cm2.



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