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What is the perimeter of a rectangle that has a diagonal of 20.8 cm and an area of 153.6 square cm detailing work from start to finish?
Let the numbers be x and y:-
If: x+y = 432.64
Then: y = 432.64-x
If: xy = 23592.96
Then: x(432.64-x) = 23592.96
So: 432.64x -x^2 = 23592.96 => 432.64x -x^2 -23592.96 = 0
Using the quadratic equation formula: x = 368.64 or x = 64 meaning y = 64
Square root of 368.64 is 19.2 and the square root of 64 is 8
Therefore perimeter: 2(19.2+8) = 54.4 cm
Check: 19.2^2 + 8^2 = 432.64 and its square root is 20.8 cm
Check: 19.2*8 = 153.6 square cm
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