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The square root of 18225 is 135

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Q: What is the square root of 18225?
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What is the sum of the lengths of the diagonals within a rhombus that has a perimeter of 78 cm and an area of 270 square cm showing how answer is worked out?

The rhombus will consist of 4 right angle triangles each having an hypotenuse of 19.5 cm and an area of 67.5 square cm Square 19.5 and square (2*67.5) then find two numbers each of which have been squared that have a sum of 380.25 and a product of 18225 Let the numbers be x and y:- If: x+y = 380.25 Then: y = 380.25-x If xy = 18225 Then: x(380.25-x) = 18225 So: 380.25x -x^2 -18225 = 0 Solving the above quadratic equation: x = 324 or x = 56.25 meaning y = 56.25 Square root of 324 = 18 and square root of 56.25 = 7.5 which are sides of triangles Therefore sum of diagonals: 36+15 = 51 cm Check: 0.5*36*15 = 270 square cm Check: 18^2 + 7.5^2 = 380.25 and its square root is 19.5 Check: 4*19.5 = 78 cm which is the perimeter


What is the perimeter of a rectangle that has a diagonal of 19.5 cm and an area of 135 square cm?

First find two numbers when each are squared have a sum of 380.25 and a product of 18225. Let the numbers be x and y:- If: x+y = 380.25 then y = 380.25 -x If: xy = 18225 then x(380.25 -x) = 18225 Expanding brackets and transposing terms: 380.25x -x^2 -18225 = 0 Using the quadratic equation formula: x = 324 or x = 56.25 Square roots of 324 and 56.25 are 18 and 7.5 respectively Therefore perimeter of rectangle is: 2*(18+7.5) = 51 cm


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