Rhombus and diagonals

The a rhombus area is 150 cm2 and the ratio of the diagonals is 3:4. Calculate the length of its height.

Correct result:

h =  12 cm

Solution:

S=150 u1:u2=3:4 S=u1 u2/2 u1=3k u2=4k S=3k⋅ 4k/2 S=6 k2 k=S/6=150/6=5 u1=3k=3⋅ 5=15 u2=4k=4⋅ 5=20 a2=(u1/2)2+(u2/2)2=(15/2)2+(20/2)2=6254=156.25 a=(u1/2)2+(u2/2)2=(15/2)2+(20/2)2=252=12.5 S=ah h=S/a=150/12.5=12 cm

Try another example


We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
avatar




Tips to related online calculators
Check out our ratio calculator.
Pythagorean theorem is the base for the 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   video2   video3

Next similar math problems:

  • Rhombus
    kosostvorec_1 The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height
  • Diamond diagonals
    kosostvorec Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square, and the side length is 13 cm.
  • Rectangle 3-4-5
    diagonal_rectangle_1 The sides of the rectangle are in a ratio of 3:4. The length of the rectangle diagonal is 20 cm. Calculate the content of the rectangle.
  • ISO triangle
    rr Calculate the area of an isosceles triangle KLM if its sides' length is in the ratio k:l:m = 4:4:3 and has perimeter 377 mm.
  • Diamond diagonals
    kosodlznik_2 Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
  • Diamond diagonals
    kosostvorec_9 Calculate the diamond's diagonal lengths if its content is 156 cm2 and the side length is 13 cm.
  • Diagonals of a rhombus 2
    rhombus3_4 One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm2, find the side of the rhombus.
  • Diagonals in diamons/rhombus
    diamonds Rhombus ABCD has side length AB = 4 cm and a length of one diagonal of 6.4 cm. Calculate the length of the other diagonal.
  • Two diagonals
    koso_2 The diagonals of the diamond EFGH have lengths in the ratio 1: 2. What is the circumference of a rhombus if the longer of the diagonals is 8 cm long?
  • Isosceles trapezoid
    lichobeznik_5 Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high.
  • Rhombus and diagonals
    rhombus-diagonals The lengths of the diamond diagonals are e = 48cm, f = 20cm. Calculate the length of its sides.
  • Cuboid face diagonals
    face_diagonals_1_1 The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid.
  • Diagonals
    koso_uhlopricky Given a rhombus ABCD with a diagonalsl length of 8 cm and 12 cm. Calculate the side length and content of the rhombus.
  • Rhombus
    rhombus Calculate the perimeter and area of ​​a rhombus whose diagonals are 39 cm and 51 cm long.
  • Trapezoid - intersection of diagonals
    intersect_trapezoid_diagonals In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate the trapezoid area.
  • Rhombus diagonal
    rhombus2_1 Area of rhombus is 224. One diagonal measures 33, find length of other diagonal.
  • A square
    rhombus3_3 A square with a length of diagonals 12cm give: a) Calculate the area of a square b) rhombus with the same area as the square, has one diagonal with a length of 16 cm. Calculate the length of the other diagonal.