Inscribed rectangle

What is the perimeter of a rectangle that is inscribed in a circle whose diameter is 5 dm long?
Answer: 14 dm

Result

p =  12.761 dm

Solution:

D=5 dm r=D/2=5/2=52=2.5 dm  x=r/3=2.5/3≐56≐0.8333 dm y=r2−x2=2.52−0.83332≐2.357 dm  p=4⋅ (x+y)=4⋅ (0.8333+2.357)≐12.7614≐12.761 dmD=5 \ \text{dm} \ \\ r=D/2=5/2=\dfrac{ 5 }{ 2 }=2.5 \ \text{dm} \ \\ \ \\ x=r/3=2.5/3 \doteq \dfrac{ 5 }{ 6 } \doteq 0.8333 \ \text{dm} \ \\ y=\sqrt{ r^2 - x^2 }=\sqrt{ 2.5^2 - 0.8333^2 } \doteq 2.357 \ \text{dm} \ \\ \ \\ p=4 \cdot \ (x+y)=4 \cdot \ (0.8333+2.357) \doteq 12.7614 \doteq 12.761 \ \text{dm}

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Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 3 comments:
#
Dr Math
not exact solution, because rectangle have two different size

#
Nestor
The solution is ambiguous. Where does x = r/3 came from?

1 year ago  1 Like
#
Dr Math
the solution is ok, bud problem is wrongly formulated.  x = r/3 is assumed to be something calculated. The solution is picked only one from infinity many solutions.

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