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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

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Q: What is the perimeter of a rhombus when one of its diagonals is greater than the other diagonal by 5 cm with an area of 150 square cm showing key aspects of work?

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I'm some cases yes while in others no :)

Let the diagonals be x+10.5 and x:- Area: 0.5*(x+10.5)*x = 67.5 Rearranging terms: x^2 +10.5x -135 = 0 Using the quadratic equation formula: x has a positive value of 7.5 Therefore diagonals are: 18 and 7.5 The rhombus will have 4 interior right angle triangles with sides of 9 and 3.75 Using Pythagoras' theorem each hypotenuse side is 9.75 Perimeter of the rhombus: 4 times 9.75 = 39 cm

The shortest path between two points is a straight line. This is a mathematical fact, which can be proven in another question.The diagonal of a quadrilateral is a straight line between two opposing (non-adjacent) vertices. The perimeter of a quadrilateral will include two separate paths between the same vertices. The difference is that these two paths are each composed of two linked line segments, so each of these paths will be longer than the diagonal.Therefore, the length of the perimeter of a quadrilateral will be greater than twice the length of either diagonal.

Of course, a rectangle can have a greater perimeter and a greater area. Simply double all the sides: the perimeter is doubled and the area is quadrupled - both bigger than they were.

Yes.

The diagonal line of a rectangle for example is greater than its length.

yes it will have a greater area

It depends on the sizes of the two shapes.

No it depends on the size of the polygon

No the area is almost always greater.

yes it can; a rectangle 5 by 2 has perimeter 14 and area 10 for example; a rectangle 10 by 2 has perimeter 24 and area 20, both greater.

No. A diagonal goes from corner to opposite corner, which will always be a longer distance than the side length. You can use Pythagoras' theorem to work out the length of the diagonals. It will be the square root of (a2+b2) where a and b are the long and short side lengths of the rectangle respectively. The result will clearly be greater than either a or b.

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