Inscribed rectangle

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

Correct result:

p =  12.7614 dm

Solution:

$$\begin{gathered} D=5\text{ dm } \\ r=D\mathrm{/}2=5\mathrm{/}2={\displaystyle \frac{5}{2}}=2.5\text{ dm } \\ x=r\mathrm{/}3=2.5\mathrm{/}3={\displaystyle \frac{5}{6}}\doteq 0.8333\text{ dm } \\ y=\sqrt{r^2-x^2}=\sqrt{2.5^2-0.8333^2}\doteq 2.357\text{ dm } \\ p=4\cdot (x+y)=4\cdot (0.8333+2.357)=12.7614\text{ dm} \end{gathered}$$

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Showing 3 comments:

Dr Math

not exact solution, because rectangle have two different size

2 years ago  Like

Nestor

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

2 years ago  1 Like 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.

2 years ago  Like

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