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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?
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
What else can I help you with?
What is the ratio of the diagonals of a Kite?
In a kite, the diagonals intersect at right angles, and one of the diagonals bisects the other. The ratio of the lengths of the diagonals can vary depending on the specific dimensions of the kite, but generally, the longer diagonal (which connects the vertices of the unequal angles) is greater than the shorter diagonal (which connects the vertices of the equal angles). There isn't a fixed ratio applicable to all kites, as it depends on their specific dimensions.
What is the perimeter of a rhombus when one diagonal is greater than the other diagonal by 10.5 cm and has an area of 67.5 square cm?
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
Will a rectangle with a greater perimeter also have a greater areea?
Yes.
What polygon Has at least one diagonal with the points outside the polygon?
A polygon that has at least one diagonal with points outside the polygon is known as a concave polygon. In a concave polygon, at least one interior angle is greater than 180 degrees, which causes the diagonal connecting two non-adjacent vertices to extend outside the shape. This characteristic differentiates concave polygons from convex polygons, where all diagonals remain inside the figure.
How diagonals intersect at a given vertex that is n-gon?
A 3-gone does not have diagonals. The two diagonals of a 4-gon meet at a point. For all values greater than 4, the diagonals of an n-gon need not necessarily meet at a single point.
Is the sum of the lengths of the diagonals of a polygon greater than the perimeter of the polygon?
I'm some cases yes while in others no :)
What is the perimeter of a rhombus when one diagonal is greater than the other diagonal by 10.5 cm and has an area of 67.5 square cm?
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
Prove that the perimeter of a quadrilateral is greater than the sum of the length of its diagonal?
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.
Can a rectangle have a greater perimeter and also have a greater area?
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.
Are diagonals equal to side lengths of rectangles?
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.
Will a rectangle with a greater perimeter also have a greater areea?
Yes.
What polygon Has at least one diagonal with the points outside the polygon?
A polygon that has at least one diagonal with points outside the polygon is known as a concave polygon. In a concave polygon, at least one interior angle is greater than 180 degrees, which causes the diagonal connecting two non-adjacent vertices to extend outside the shape. This characteristic differentiates concave polygons from convex polygons, where all diagonals remain inside the figure.
Is a greater perimeter going to have a greater area can you show a picture?
yes it will have a greater area
Is the hexagon perimeter greater than the perimeter of the pentagon?
It depends on the sizes of the two shapes.
Can a rectangle have a greater perimeter than another one but have a greater area too?
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.
How diagonals intersect at a given vertex that is n-gon?
A 3-gone does not have diagonals. The two diagonals of a 4-gon meet at a point. For all values greater than 4, the diagonals of an n-gon need not necessarily meet at a single point.
Is perimeter always greater than the area?
No the area is almost always greater.
