What is the smallest diameter that a log should have so that a rectangle with a cross-section can be cut out of it

| June 15, 2021 | education

What is the smallest diameter that a log should have so that a rectangle with a cross-section can be cut out of it, the length of the sides of which is 2: 1, and the area is 1000 cm ^ 2.

1) Denote by variable x the length of the shorter side. The length of the longer side is 2x. Let’s compose and solve the equation, knowing that the area of the rectangle is 1000 cm2.

x * 2x = 1000.

2x ^ 2 = 1000.

x ^ 2 = 1000/2 = 500.

x = √500.

2x = 2√500.

2) The diameter of a circle circumscribed about a rectangle can be calculated using the formula:

d = √ (a ^ 2 + b ^ 2), where a and b are the lengths of the sides of the rectangle.

d = √ (a ^ 2 + b ^ 2) = √ (√500 ^ 2 + (2√500) ^ 2) = √ (500 + 4 * 500) = √2500 = 50 cm.

Answer: The log must have a minimum diameter of 50 cm.



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