Is it possible to cut a beam from a log with a diameter of 30 cm, the cross-section of which is a square with a side of 24 cm?

In order for a beam with a square cross-section to be as large as possible, it is necessary that the square, which in the cross-section of the beam, fits into the circumference of the cross-section of the log. So we need to find out what is the maximum side of the square, which can be in a circle with a diameter of 30 cm. To find this, remember what the circle and the square inscribed in it have in common: The diameter of the circle is equal to the diagonal of the square. Then, by the Pythagorean theorem, we write: a ^ 2 + a ^ 2 = 30 ^ 2, where a is the side of the square. From here we find a: 2 * a ^ 2 = 900 a ^ 2 = 450 a = √ (450) a = 15 * √ (2) a = -15 * √ (2) We discard the negative root, because measurements of dimensions cannot be negative: a = 15 * √ (2) We found out the maximum side of the square of the cross-section of the beam that can be cut out of the log. Compare 24 and 15 * √ (2): 24 = √ (576) 15 * √ (2) = √ (450) 24> 15 * √ (2), so we cannot cut a beam with a square cross section with a side of 24 cm …
Answer: no.