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ollegr [7]
3 years ago
12

What is the side length of the largest square that can fit into a circle with a radius of 5 units?

Mathematics
1 answer:
Mariana [72]3 years ago
5 0
So 1st consider that it's a square! That's very important. So for a square, all 4 sides are equal.

And now considering that the given information is the diameter. So any angle made at the circle extended from the 2 points of diameter gives an angle of 90°

Now consider one triangle. So we already know that 2 sides of the triangle are equal (because they are 2 sides of a square) , has a side of 10 (diameter) and and angle of 90°. So remaining 2 angles are 45°

Now solve it by applying

\sin(45) \: \: \: \: = x \div 10 \\ (1 \div \sqrt{2} ) = (x \div 10) \\ 10 \div \sqrt{2} \: = x
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