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#1
-1

The Pythagoras's theorem is leg^2 +leg^2 = hyp^2

squares are two right triangles

since we know a square is 5 on both sides, we can do

5^2 + 5^2 = hyp^2

25 +25 = hyp ^2

50 = hyp ^2

sq root of 50 = hyp

so the diagonal of the square is sq root of 50, and the sides are 5.

since the sq root of 50 is smaller than 9, and 5 is smaller than 9, we have proven that the square can fit in the circle

Guest Nov 16, 2017
#2
-1

The largest square that will fit inside the circle will have a side, S,  of

4.5^2 + 4.5^2  = S^2  simplify

2 *4.5^2  = S^2

√[ 4.5^2 * 2 ]  = S^2      take the square root

√4.5^2 √ 2   = s

4.5√2  =  S  ≈ 6.36 cm    so...a square with a side of 5 will fit inside the circle.......

CPhill 3 hours ago

Guest Nov 16, 2017

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