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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?
Wiki User
∙ 9y ago
The area of rectangle is : 13832.797999999999
Vivianne Schamberger
Wiki User
∙ 9y agoThese are the key stages:
1) Write an equation that defines the perimeter on the basis of length and width. (The perimeter is the sum of the four sides.) Replace the known perimeter.
2) Write an equation that defines the diagonal, once again based on the length and width. (Use the Pythagorean Theorem for this.) Replace the known diagonal.
3) Solve the two equations simultaneously. For example, you might solve the first equation for length, and replace this in the second equation. This will give you length and width.
4) Multiply length and width to get the area.
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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 and perimeter of a rectangle when its sides are in the ratio 8 to 15 with an area of 367.5 square cm showing all work in step by step stages?
1 Let the sides be 8x and 15x 2 So: 8x*15x = 367.5 or 120x2 = 367.5 3 Divide both sides by 120 and then square root both sides 4 Therefore: x = 1.75 so sides are 8*1.75 = 14 cm and 15*1.75 = 26.25 cm 5 Check: 14*26.25 = 367.5 square cm 6 Using Pythagoras: 142+26.252 = 885.0625 and its square root is 29.75 7 Diagonal = 29.75 cm 8 Perimeter = (2*14)+(2*26.25) = 80.5 cm
What is the length of the diagonal of a rectangle in cm whose height is greater than its width by 13.5 mm and has an area of 2187 square mm showing key stages of work?
1 13.5 mm = 1.35 cm and 2187 sq mm = 21.87 sq cm2 Let the height be x+1.35 and the width be x3 (x+1.35)*x = 21.874 x2+1.35x-21.87 = 05 Solving the quadratic equation gives x a positive value of 4.056 Therefore: width = 4.05 cm and height = 5.4 cm7 Using Pythagoras: diagonal = 6.75 cm8 Check: 4.05*5.4 = 21.87 square cm = 2187 square mm
What is the hypotenuse and perimeter of a right angle triangle when one side is greater than the other side by 4.75 cm with an area of 135.375 square cm showing all work in logical stages?
1 Let the sides be: x+4.75 and x2 If: 0.5*(x+4.75)*x = 135.3753 Then: x2+4.75x-270.75 = 04 Using the quadratic equation formula: x has a positive value of 14.255 Therefore: sides are 14.25+4.75 = 19 cm and 14.25 cm6 Using Pythagoras: 192+14.252 = 564.0625 and its square root is 23.757 Hypotenuse: 23.75 cm8 Perimeter: 23.75+19+14.25 = 57 cm9 Check: 0.5*19*14.25 = 135.375 square cm
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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 and perimeter of a rectangle when its sides are in the ratio 8 to 15 with an area of 367.5 square cm showing all work in step by step stages?
1 Let the sides be 8x and 15x 2 So: 8x*15x = 367.5 or 120x2 = 367.5 3 Divide both sides by 120 and then square root both sides 4 Therefore: x = 1.75 so sides are 8*1.75 = 14 cm and 15*1.75 = 26.25 cm 5 Check: 14*26.25 = 367.5 square cm 6 Using Pythagoras: 142+26.252 = 885.0625 and its square root is 29.75 7 Diagonal = 29.75 cm 8 Perimeter = (2*14)+(2*26.25) = 80.5 cm
How do you find the perimeter of a rectangle whose diagonal is 17.55 cm with an area of 109.35 square cm in step by step stages?
Another Answer:-Let the dimensions of the rectangle be x and y which are squared and square the diagonal and the area:-Using Pythagoras: x+y = 308.0025 => y = 308.0025-xArea: xy = 11957.4225 => x(308.0025 -x) = 11957.4225So it follows: 308.0025x -xsquared -11957.4225 = 0Solving the quadratic equation: x = 262.44 or x = 45.5625Square root of both number: x = 16.2 and x = 6.75By substitution: x = 16.2 and y = 6.75Perimeter: 2(16.2+6.75) = 45.9 cmCheck: 16.2*6.75 = 109.35 square cm
What is the area of a rectangle when one side is greater than the other side by 19.25 cm and has a diagonal of 46.75 cm showing key stages of work?
Suppose the length and breadth of the rectangle are L and B cm respectively, and the diagonal is D cm. Then, by Pythagoras, D2 = L2 + B2 So that 46.752 = (B + 19.25)2 + B2 = B2 + 38.5*B + 19.252 + B2 2B2 + 38.5*B - 1815 = 0 So B = 22 or -41.25 cm Since B cannot be negative, B = 22 cm. And therefore, the area is L*B = (22 + 19.25)*22 cm2 = 907.5 cm2
What is the length of the diagonal of a rectangle in cm whose height is greater than its width by 13.5 mm and has an area of 2187 square mm showing key stages of work?
1 13.5 mm = 1.35 cm and 2187 sq mm = 21.87 sq cm2 Let the height be x+1.35 and the width be x3 (x+1.35)*x = 21.874 x2+1.35x-21.87 = 05 Solving the quadratic equation gives x a positive value of 4.056 Therefore: width = 4.05 cm and height = 5.4 cm7 Using Pythagoras: diagonal = 6.75 cm8 Check: 4.05*5.4 = 21.87 square cm = 2187 square mm
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1 Let its height be x+1.45 and its base be x2 So: 0.5*(x+1.45)*x = 12.615 multiply both side by 23 Therefore: x2+1.45x-25.23 = )4 Using quadratic equation formula gives x a positive value of 4.355 It follows: height = 5.8 and base = 4.356 Using Pythagoras: hypotenuse = 7.257 Perimeter: 5.8+4.35+7.25 =17.4 cm
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