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Let the other diagonal be x

If: 0.5*12*x = 30 then x = 60/12 => x = 5

The rhombus has four interior right angle triangles with lengths of 6 cm and 2.5 cm

Using Pythagoras each equal sides of the rhombus works out as 6.5 cm

Perimeter: 4*6.5 = 26 cm

Q: What is the perimeter of a rhombus whose area is 30 square cm and whose largest diagonal is 12 cm showing work?

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Converting perimeter, the linear distance around the outside of a shape, to the area of the shape has no "general" formula. Each shape has its own characteristics, and we must apply different ways to find the area enclosed by a given perimeter for each shape. It is the geometry of the shape that will direct our efforts. Let's look at some shapes for a given perimeter and see what's up. If we have a square with a perimeter of 20, we know we have a shape with 4 equal sides which add up to 20. Our 20 divided by 4 is 5. That's 4 sides of length 5 (5 + 5 + 5 + 5 = 20), and the area equal to the square of a side, or 52, or 25 square units. What about a rectangle with a perimeter of 20? Is it a shape with a length of 6 and a width of 4, or it is a length of 8 and a width of 2? Both have the same perimeter, a perimeter of 20. But one has an area of 6 x 4 = 24 square units, and the other has an area of 8 x 2 = 16 square units. See the problem? Fasten your seatbelt. It gets worse. What if we have a circle with a perimeter of 20? The perimeter of a circle is called its circumference, and its equal to pi times the diameter, or pi times 2 times the radius (because a diameter is 2 radii). In the case of the circle, its area is pi times the square of the radius. If we do some math here, we'll find the area of the circle is 100 divided by pi. (We left out showing the work.) That makes the area of the circle about 31.85 square units. We've just converted the perimeter of 4 different geometric shapes into areas. And no two are alike. It wasn't too tough with the square, but we hit a snag with the rectangle. We needed more data. We were lucky with the circle. As shapes become more complex, we need "clues" to solve perimeter-to-area "conversions" for the shapes. There are rules and methods for discovering the area of a shape based on the perimeter and a little bit of other data. And we need bits of data in addition to just the perimeter of the shape, the primary one being the type of geometric figure itself. What if it was a kite? A rhombus or parallelogram? An ellipse? See how "complicated" it can get? As we pick our way through geometry, we start to gain some insight into how we can find out things about these shapes to define and measure them. Good luck picking up the tools to handle the job.

Impossible to answer ! You stated the perimeter, and the area, but - since the internal angles simply need to add up to 360 degrees, the angles could literally be anywhere between 1 & 179 degrees. This means that the lengths of the diagonals could be any number of measurements !Another Answer:-The rhombus will consist of 4 right angle triangles each having an hypotenuse of 14.5 cm and an area of 52.5 square cm.Square 14.5 and square (2*52.5) then find two numbers each of which have been squared that have a sum of 210.25 and a product of 11025Let the squared numbers be x and y:-If: x+y = 210.25Then: y = 210.25-xIf: xy = 11025Then: x(210.25-x) = 11025So: 210.25x -x^2 -11025 = 0Solving the above quadratic equation: x = 110.25 or x = 100 meaning y = 100Square root of 110.25 = 10.5 and square root of 100 = 10Therefore the lengths of the diagonals are 21 cm and 20 cmCheck: 0.5*21*20 = 210 square cmCheck: 10.5^2 + 10^2 = 210.25 and its square root is 14.5 cmCheck: 4*14.5 = 58 cm which is the perimeter of the rhombus

Let its sides be x and rearrange the diagonal formula into a quadratic equation:- So: 0.5(x^2-3x) = 252 Then: x^2-3n-504 = 0 Solving the quadratic equation: gives x a positive value of 24 Therefore the polygon has 24 sides irrespective of it being irregular or regular

Using the diagonal formula when n is number of sides :- If: 0.5*(n^2-3n) = 189 Then multiplying both sides by 2 and subtracting both sides by 2*189 So: n^2-3n-378 = 0 Solving the above quadratic equation gives n a positive value of 21 Sum of interior angles: (21-2)*180 = 3420 degrees

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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.

Here is what you are supposed to do: * Convert to consistent units. For example, convert the cm to mm. * Write an equation for the diagonal (in terms of length and width). Replace the known diagonal. * Write an equation for the area, in terms of length and width. * Solve the two equations simultaneously. * Calculate the perimeter.

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

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

The area of rectangle is : 13832.797999999999

Double the area and find 2 numbers that have a sum of 42.5 and a product of 375 which will work out as 30 and 12.5 by using the quadratic equation formula. Therefore the diagonals are of lengths 30 and 12.5 which will intersect each other half way at right angles forming 4 right angle triangles inside the rhombus with sides of 15 cm and 6.25 cm Using Pythagoras' theorem each out side length of the rhombus is 16.25 cm and so 4 times 16.25 = 65 cm which is the perimeter of the rhombus.

Let the diagonals be x and yIf: x+y = 24.5 then y = 24.5-xIf: 0.5xy = 73.5 then 0.5x(24.5-x) = 73.5So: 24.5x -x^2 -147 = 0Solving the above quadratic equation: x = 14 or 10.5The rhombus will consist of 4 right angles of base 5.25 and height 7Using Pythagoras' theorem each side of the rhombus is 8.75 cmTherefore its perimeter is: 4*8.75 = 35 cm

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

Here are the key aspects of work; I'll leave the details of the calculation to you. 1) Write an equation for the area, in terms of variables "w" and "h" (for width and height). 2) Write an equation for the length of the diagonal, in terms of "w" and "h". (Hint: Use the Pythagorean Theorem.) 3) Solve the two equations. 4) Calculate the perimeter, based on length and width.

The area of rectangle is : 13832.797999999999

Change the perimeter into cm which is 93.24 cm and let its length be x with its width being y thus it followa that:- 1 Perimeter: 2x+2y = 93.24 => y = 46.62-x 2 Area: xy = 532.2672 => x(46.62-x) = 532.2672 3 And so area: 46.62x-x^2-532.2672 = 0 4 Using the quadratic equation formula: x = 26.64 and y = 19.98 5 Using Pythagoras' theorem: diagonal = 33.3 cm or 333 mm

Let the shorter side be 'a'. Then the longer side is 2a + 3.5To find the perimeter we add the 4 sides: a+a+(2a+3.5) + (2a+3.5) = 6a+7Now we know the perimeter is 59.5cmSo 6a+7=59.5==> 6a = 52.5==> a = 52.5 ÷ 6 = 8.75So the shorter side is 8.75 and the longer side is (2 * 8.75) + 3.5 = 21. (where * means multiply)Now to find the diagonal, we use Pythagoras a^2 + b^2 = c^2 (where ^2 means to the power of 2 or squared)So substituting the two sides of the rectangle,c^2 (the diagonal) = 21^2 + (8.75)^2 = 441 + 76.5625 = 517.5625==> c = sq rt (517.5625) = 27.75cmAdditional Information:-All of the above is correct except for the fact that the square root of 517.5625 is 22.75cm which is the length of the diagonal