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 =  12.761 dm

Solution:

D=5 dm r=D/2=5/2=52=2.5 dm  x=r/3=2.5/3560.8333 dm y=r2x2=2.520.833322.357 dm  p=4 (x+y)=4 (0.8333+2.357)=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)=12.761 \ \text{dm}



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

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.

avatar









Tips to related online calculators
See also our right triangle calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1

Next similar math problems:

  • Table
    stol The circumference of the rectangle table is 420 cm. Length to width ratio is 5:2 . Calculate table dimensions and dimensions reduced in the ratio 3:5
  • Playground
    playground The land for the construction of the school playground has the shape of a rectangle with a shorter side of 370 m. Its other side is 260 m longer. How many meters of the fence does the school need to buy on the fencing playground?
  • Perimeters
    triangles A rectangle has a perimeter of 16p centimeters, it had a width of 2p centimeters. Each side of an equilateral triangle is 1/2 the length of the rectangle. Find the total perimeter of the rectangle and the triangle if p=8.
  • Playground
    playground_fencing Rectangular playground is fenced with 38 m long netting. Its width is 7 m. Calculate its length.
  • Circles
    three-circles Three circles of radius 95 cm 78 cm and 64 cm is mutually tangent. What is the perimeter of the triangle whose vertices are centers of the circles?
  • Circle
    circle_1 What is the radius of the circle whose perimeter is 6 cm?
  • The diameter
    circles The diameter of a circle is 4 feet. What is the circle's circumference?
  • Land
    12-13-5-triangle Rectangular triangular land has area 30 square meters and 12 meters long leg. How many meters of the fence do you need for fencing this land?
  • Find the
    kruh Find the radius of the circular base of the vessel, whose perimeter is 2.51 m. Write the result to one decimal place in meters. Via the π sign - Ludolph's number
  • Circle - simple
    kruh The circumference of a circle is 198 mm. How long in mm is its diameter?
  • Circle r,D
    bavlnka Calculate the diameter and radius of the circle if it has length 26.59 cm.
  • Thales
    circles_1 Calculate the length of the Thales' circle described to right triangle with hypotenuse 44.2 cm.
  • Triangle perimeter
    triangle_vysky_3 Calculate the triangle perimeter whose sides are in ratio 3: 5: 7 and the longest side is 17.5 cm long.
  • Sides of triangle
    rr_triangle2 Triangle circumference with two identical sides is 117cm. The third side measures 44cm. How many cms do you measure one of the same sides?
  • An equilateral triangle
    equilateral_triangle The perimeter of an equilateral triangle is 33cm. How long is each side?
  • Triangle P2
    1right_triangle Can triangle have two right angles?
  • Calculate
    equilateral_triangle2 Calculate the length of a side of the equilateral triangle with an area of 50cm2.