Rectangle 35

Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length.

Correct result:

S =  360 cm2

Solution:

u=30 cm a=2b u2=a2+b2 S=ab=360 cm2 u2=(2b)2+b2 u2=5 b2 b=u/5=30/5≐6 5≐13.4164 a=2⋅ b=2⋅ 13.4164≐12 5≐26.8328 S=a⋅ b=26.8328⋅ 13.4164=360 cm2 v=a2+b2=26.83282+13.41642=30 cmu=30 \ \text{cm} \ \\ a=2b \ \\ u^2=a^2 + b^2 \ \\ S=ab=360 \ \text{cm}^2 \ \\ u^2=(2b)^2 + b^2 \ \\ u^2=5 \ b^2 \ \\ b=u/\sqrt{ 5 }=30/\sqrt{ 5 } \doteq 6 \ \sqrt{ 5 } \doteq 13.4164 \ \\ a=2 \cdot \ b=2 \cdot \ 13.4164 \doteq 12 \ \sqrt{ 5 } \doteq 26.8328 \ \\ S=a \cdot \ b=26.8328 \cdot \ 13.4164=360 \ \text{cm}^2 \ \\ v=\sqrt{ a^2+b^2 }=\sqrt{ 26.8328^2+13.4164^2 }=30 \ \text{cm}

Try another example


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!


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

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Check out our ratio calculator.
Pythagorean theorem is the base for the right triangle calculator.
Tip: Our volume units converter will help you with the conversion of volume units.

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   video2

Next similar math problems:

  • Rectangle
    obdelnik_1 The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle.
  • Diagonal to area
    rectangle_5 Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
  • Rectangle diagonal
    rectnagles_3 The rectangle, one side of which is 5 cm long, is divided by a 13 cm diagonal into two triangles. Calculate the area of one of these triangles in cm2.
  • Rectangle area
    rectangles_5 The length of a rectangle of x units is increased by 10% and its width of y units is increased by 15%. What is the ratio of the area of the old rectangle to the area if the new rectangle?
  • Surveyor
    totalna-stanica Calculate the area of ​​what may vary rectangular, if it focused by surveyor and found the dimensions 18 x 15 m while in each of the four joint points can be position deviation 25 cm?
  • Sidewalk
    bazen_sivy In the garden, a 1-meter-wide sidewalk will be paved with tiles around the block-shaped pool. In the picture, the sidewalk is shown in gray. The dimensions of the bottom of the pool are 8.5 meters and 6 meters. The height of the pool walls is 2 meters.
  • Enlarged rectangle
    rectangle_10 The rectangle with dimensions of 8 cm and 12 cm is enlarged in a ratio of 5:4. What are the circumference and the area of the enlarged rectangle?
  • Screens
    tv2_3 The area of a 25 inch TV screen is 300 inch² the area of a 40 inch TV screen is 768 inch². The area of the smaller screen is what percent of the area of the larger screen?
  • Tv screen
    tv2 The size of a tv screen is given by the length of its diagonal. If the dimension of a tv screen is 16 inches by 14 inches, what is the size of the tv screen?
  • Umbrella
    dazdnik Can umbrella 75 cm long fit into a box of fruit? The box has dimensions of 390 mm and 510 mm.
  • Rhombus diagonal
    rhombus2_1 Area of rhombus is 224. One diagonal measures 33, find length of other diagonal.
  • Trapezium
    trapezium_1 The area of trapezium is 35 cm2. Find its altitude if the bases are 6cm and 8 cm.
  • Pile of sand
    pile_sand A large pile of sand has been dumped into a conical pile in a warehouse. The slant height of the pile is 20 feet. The diameter of the base of the sand pile is 31 feet. Find the volume of the pile of sand.
  • The right triangle
    rt_tr540 The right triangle ABC has a leg a = 36 cm and an area S = 540 cm2. Calculate the length of the leg b and the median t2 to side b.
  • Equilateral triangle
    rs_triangle_1 The equilateral triangle has a 23 cm long side. Calculate its content area.
  • Median in right triangle
    rt_triangle In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
  • Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?