Gnpth
What is area of square LMNO?
(1) The longest line segment that can be drawn through any two points on the perimeter of square LMNO is \(4\sqrt{2}\).
(2) When a circle is inscribed in square LMNO, the longest line segment connecting two points on the circumference of the circle that can be drawn has a length of 4.
Good but relatively an easy question. Thank you for posting.
What is area of square LMNO?(1) The longest line segment that can be drawn through any two points on the perimeter of square LMNO is \(4\sqrt{2}\).
The longest line segment that can be drawn in a square is the diagonal:
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Hence this statement simply says that the length of the diagonal is \(4\sqrt{2}\): \(area_{square}=\frac{d^2}{2}=16\). Sufficient.
(2) When a circle is inscribed in square LMNO, the longest line segment connecting two points on the circumference of the circle that can be drawn has a length of 4.
The longest line segment that can be drawn in a circle is the diameter:
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Now, the diameter of an inscribed circle equals to the side of a square: \(area_{square}=side^2=16\). Sufficient.
Answer: D.
Hope it's clear.