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What is the perimeter of a rhombus when its diagonals add up to 24.5 cm and has an area of 73.5 square cm showing work?
Wiki User
∙ 8y ago
Let the diagonals be x and y:-
If: x+y = 24.5 then y = 24.5-x
If: 0.5xy = 73.7 then 0.5x(24.5-x) = 73.5
So: 24.5x -x^2 -147 = 0
Solving the quadratic equation: x = 14 or x = 10.5
The rhombus will then consist of 4 right angle triangles of base 5.25 and height 7
Using Pythagoras: 5.25^2+7^2 = 76.5625 and its square root is 8.75
Therefore the perimeter of the rhombus: 4*8.75 = 35 cm
Wiki User
∙ 8y ago
Wiki User
∙ 8y agoSuppose the diagonals are of length 2a and 2bthen sum of diagonals = 2*a + 2*b = 24.5 = 49/2 => a + b = 49/4
Also, area = 2*a*b = 73.5 = 147/2
Suppose the side of the rhombus is c. Then
c^2 = a^2 + b^2 = (a + b)^2 - 2*a*b = (49/4)^2 - 147/2 = 1225/16
=> c = 35/4
Then, perimeter = 4*c = (35/4)*4 = 35 cm
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The area of rhombus with diagonals 28Cm square and 28Cm is: 392 cm2
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Are diagonals of a rhombus parallel?
noNo, the diagonals of a rhombus are perpendicular to each other.Unless the rhombus is regular (and called a square) the diagonals are of different lengths.
Area of rhombus with diagonals 28Cm square and 28Cm?
The area of rhombus with diagonals 28Cm square and 28Cm is: 392 cm2
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What is the perimeter of a rhombus when the diagonals equal 30 and 40 inches?
Each side S = square root ( 152 + 202 ) = 25The perimeter will then be 4 x S = 100
What figure always have perpendicular diagonals?
Square, rhombus or a kite.
Does a rhombus have equal diagonals?
No. If they were equal the rhombus would become a square.
What is the area of a rhombus when one of its diagonals is 11.8 cm in length and has a perimeter of 29 cm showing work and answer?
Perimeter = 29 cm so each side is 7.25 cm. The triangle formed by the diagonal and two sides has sides of 7.25, 7.25 and 11.8 cm so, using Heron's formula, its area is 24.9 square cm. Therefore, the area of the rhombus is twice that = 49.7 square cm.
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Yes, if they are a square.
