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What is the perimeter of a rectangle whose diagonal is 17.55 cm with an area of 109.35 square cm showing key aspects of work?
DavidGambell
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.
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∙ 9y ago
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What is the perimeter of a rectangle which has a diagonal of 8.50 cm and an area of 3000 square mm showing work with answer?
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.
What is the area of a rectangle that has a perimeter of 61.18 cm and a diagonal of 226.1 mm showing key stages of work?
The area of rectangle is : 13832.797999999999
What is the area of a rectangle that has a perimeter of 61.18 cm and a diagonal of 226.1 mm showing work and answer?
The area of rectangle is : 13832.797999999999
What is the area of a rectangle that has a perimeter of 64.6 cm and a diagonal of 24.7 cm showing work?
The area of rectangle is : 1595.62
What is the diagonal length of a rectangle whose area is 212.268 square cm with a perimeter of 61.18 cm showing all work with answer?
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
What is the perimeter of a rectangle which has a diagonal of 8.50 cm and an area of 3000 square mm showing work with answer?
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.
What is the area of a rectangle that has a perimeter of 61.18 cm and a diagonal of 226.1 mm showing key stages of work?
The area of rectangle is : 13832.797999999999
What is the area of a rectangle that has a perimeter of 61.18 cm and a diagonal of 226.1 mm showing work and answer?
The area of rectangle is : 13832.797999999999
What is the area of a rectangle that has a perimeter of 64.6 cm and a diagonal of 24.7 cm showing work?
The area of rectangle is : 1595.62
What is the diagonal length of a rectangle whose area is 212.268 square cm with a perimeter of 61.18 cm showing all work with answer?
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
What is the size of the diagonal of a rectangle whose length is twice its width plus 3.5 cm and has a perimeter of 59.5 cm showing all work?
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
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?
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
What is the diagonal length of a rectangle whose perimeter is 452.2 mm with an area of 106.134 square cm showing work and answer to an appropriate degree of accuracy if necessary?
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
What is the area of a rectangle which has a diagonal of 17.55 cm and a perimeter of 459 mm showing all work?
The area of rectangle is : 8055.450000000001
What are the dimensions of a rectangle that has a perimeter of 19.8 cm and an area of 24.3 square cm showing work?
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
What is the area of a rectangle whose dimensions are in the ratio of 5 to 12 with a diagonal of 17.55 cm showing all aspects of work?
1 Let the sides be 5x and 12x2 Using Pythagoras: (5x)2+(12x)2 = 17.5523 And so: 25x2+1442 = 308.0025 => 1692 = 308.00254 Divide both sides by 169 and then square root both sides5 Therefore: x = 1.35 so sides are 5*1.35 = 6.75 cm and 12*1.35 = 16.2 cm6 Area = 6.75*16.2 = 109.35 square cm7 Check with Pythagoras: 6.752+16.22 = 308.0025 and its square root is 17.55 cm which is the rectangle's diagonal
What is the perimeter of a rhombus whose area is 30 square cm and whose largest diagonal is 12 cm showing work?
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
