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:

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

Try another example

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

Next similar math problems:

• Infinity
  In a square with side 19 is inscribed circle, the circle is inscribed next square, again circle, and so on to infinity. Calculate the sum of the area of all these squares.
• Flags
  How many different flags can be made from colors red, yellow, blue, green, white to consist of three different colors?
• Tangent 3
  In a circle with centre O radius is 4√5 cm. EC is the tangent to the circle at point D. Segment AB IS THE DIAMETER of given circle. POINT A is joined with POINT E and POINT B is joined with POINT C. Find DC if BC IS 8cm.
• Cathethus and the inscribed circle
  In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle.
• Triangle perimeter
  Calculate the triangle perimeter whose sides are in ratio 3: 5: 7 and the longest side is 17.5 cm long.
• Cylinder height
  Calculate the height of the cylinder and its surface is 2500 dm² and the bases have a diameter 5dm.
• Perimeter of the circle
  Calculate the perimeter of the circle in dm, whose radius equals the side of the square containing 0.49 dm²?
• Quarter circle
  What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
• Circle annulus
  There are 2 concentric circles in the figure. Chord of larger circle 10 cm long is tangent to the smaller circle. What are does annulus have?
• Inscribed circle
  XYZ is right triangle with right angle at the vertex X that has inscribed circle with a radius 5 cm. Determine area of the triangle XYZ if XZ = 14 cm.
• Inscribed rectangle
  The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.
• Circle inscribed
  Calculate the perimeter and area of a circle inscribed in a triangle measuring 3 , 4 and 5 cm.
• Three shapes
  1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle?
• Inscribed circle
  The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c.
• Inscribed circle
  Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC.
• Diagonals of pentagon
  Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.
• 3rd dimension
  The block has a surface of 42 dm² and its dimensions are 3 dm and 2 dm. What is the third dimension?