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Let the other diagonal be x:-

If: 0.5*x*12 = 54

Then: x = 54/6 => 9

The rhombus will consist of 4 right angles: base 4.5 cm and height 6 cm

Using Pythagoras: hypotenuses = 7.5 cm

Therefore perimeter: 4*7.5 = 30 cm

Q: What is the perimeter of a rhobus when one of its diagonals is 12 cm and has an area of 54 square cm showing work?

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It's not possible

Yes, a square is a special kind of rhombus.

A square IS always a special kind of rhombus.

Area of a kite in square units = 0.5 times the product of its diagonals

Each side S = square root ( 152 + 202 ) = 25The perimeter will then be 4 x S = 100

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It's not possible

Yes, a square is a special kind of rhombus.

Area of the rhombus: 0.5*7.5*10 = 37.5 square cm Perimeter using Pythagoras: 4*square root of (3.75^2 plus 5^2) = 25 cm

A square IS always a special kind of rhombus.

Rectangle: A quadrilateral with 4 right angles, diagonals congruent/bisecting, and opposite sides congruent, BUT ADJACENT SIDES ARE NOT CONGRUENT. Rhobus: A quadrilateral with opposite congruent angles, but adjacent angles are Not congruent, perpendicular bisecting diagonals and 4 congruent sides. Square: A quadrilateral that is a rectangle and a square with 4 right angles, diagonals congruet/bisecting that ar perpendicular, and opposites sides congruent.

Area of a kite in square units = 0.5 times the product of its diagonals

Each side S = square root ( 152 + 202 ) = 25The perimeter will then be 4 x S = 100

Perimeter: 4 times square root of (3.5^2+6^2) = 2 times square root of 193 in cm

The perimeter of a square with a diagonal of 12 centimeters is: 33.9 centimeters.In future, to find out the perimeter of a square when you only know it's diagonal, use Pythagoras or times the diagonal by 2.828427125.This number is irrational, and is like a pi for the diagonals of squares.I call it Tau.It is the relationship between the diagonal of all squares and there perimeter.

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.

It has 2 Diagonals!!!

Let the diagonals be x+5 and x:- If: 0.5*(x+5)*x = 150 sq cm Then: x2+5x-300 = 0 Solving the above by means of the quadratic equation formula: x = +15 Therefore: diagonals are 15 cm and 20 cm The rhombus has 4 interior right angle triangles each having an hypotenuse Dimensions of their sides: 7.5 and 10 cm Using Pythagoras' theorem: 7.52+102 = 156.25 Its square root: 12.5 cm Thus: 4*12.5 = 50 cm which is the perimeter of the rhombus Note: area of any quadrilateral whose diagonals are perpendicular is 0.5*product of their diagonals