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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

Q: What is the diagonal length of a rectangle with an area of 532.2672 square cm and a perimeter of 932.4 mm showing all key stages of work?

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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.

The area of rectangle is : 13832.797999999999

The area of rectangle is : 13832.797999999999

The area of rectangle is : 1595.62

Let the dimensions of the rectangle be x and y and divide its perimeter by 2:- So: x+y = 30.59 => y = 30.59 -x Area: xy = 212.268 => x(30.59 -x) = 212.268 It follows that: 30.59x - xsquared -212.268 = 0 Solving the quadratic equation: x = 19.95 or x = 10.64 By substitution: x = 19.95 and y = 10.64 Using Pythagoras: 19.95squared+10.64squated = 511.2121 The square root of 511.2121 is 22.61 cm which is the diagonal length

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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.

The area of rectangle is : 13832.797999999999

The area of rectangle is : 13832.797999999999

The area of rectangle is : 1595.62

Let the dimensions of the rectangle be x and y and divide its perimeter by 2:- So: x+y = 30.59 => y = 30.59 -x Area: xy = 212.268 => x(30.59 -x) = 212.268 It follows that: 30.59x - xsquared -212.268 = 0 Solving the quadratic equation: x = 19.95 or x = 10.64 By substitution: x = 19.95 and y = 10.64 Using Pythagoras: 19.95squared+10.64squated = 511.2121 The square root of 511.2121 is 22.61 cm which is the diagonal length

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.

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

Let the dimensions be x, y and change the perimeter into cm:- Perimeter: 2(x+y) = 45.22 cm => y = 22.61-x Area: xy = 106.134 => x(22.61-x) = 106.134 So it follows: 22.61x-x^2-106.134 = 0 Solving the above quadratic equation: x = 15.96 or x = 6.65 If: x = 6.65 then y = 15.96 Using Pythagoras: 6.65^2+15.96^2 = 298.9441 Square root of 298.9441 = 17.29 cm or 172.9 mm which is the rectangle's length

The area of rectangle is : 8055.450000000001

Divide the perimeter by 2 then find two numbers that have a sum of 9.9 and a product of 24.3 which will work out as 5.4 and 4.5 by using the quadratic equation formula. Check: 2*(5.4+4.5) = 19.8 cm which is the perimeter Check: 5.4*4.5 = 24.3 square cm which is the area Therefore the dimensions of the rectangle are: 5.4 cm and 4.5 cm

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

The diagonal is 8.5 cm and the area is 30 square cm.Let the dimensions be x and y that have been squared and square the diagonal and the area.Using Pythagoras: x+y = 72.25 => y = 72,25-xArea: xy = 900 => x(72.25-x) = 900So it follows: 72.25x - xsquared -900 = 0Solving the quadratic equation: x = 56.25 or x = 16Square root of both number: x = 7.5 and 4By substitution: x = 7.5 and y = 4Perimeter: 2(7.5+4) = 23 cmCheck: 7.5*4 = 30 square cm which is the same as 3000 square mm