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2 7 6

9 5 1

4 3 8

Q: Can sums all rows equal 15 when using 3 rows of 3 and making the diagonal rows also equal 15 using 1 through 9 only once?

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Using Pythagoras' theorem which says that the square on the hypotenuse (in this case the diagonal) is equal to the sum of the squares on the other two sides (which in the case of a square would be equal in length). so if the diagonal measured 10 units, the square on the diagonal would be 100 square units. And as this = 2*the squares on the other sides, the square on one side would be 100/2 = 50 square units. As a square has sides of equal length the square on one side is actually the area of the square. i.e. the area of a square with a diagonal of 10 units is 50 square units. or generically the area of a square with a diagonal of length 'x' = (x2)/2

Using Pythagoras: 322+362 = 2320 and the square root of this is the length of the diagonal

Using Pythagoras theorem: 53.665' correct to 3 dp

You can calculate this using the Pythagorean formula for a right triangle.

Assuming you are talking about a rectangular area, the diagonal would be found using the Pythagorean Theorem. 5^2 + 10^2 = d^2, so 125 = d^2, then take square root of both sides. This means the diagonal is approximately 11.18 feet. It is exactly 5√5 feet.

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If the vectors emanting from one corner of the rectangel are called a and b then. (a) + (b) = one diagonal (a) + (-b) = the other diagonal and |(a) + (b)| = |(a) + (-b)| (the absolute value of the diagonal's scalars are equal)

Using Pythagoras' theorem the diagonal of the rectangle is about 29.15 units in length

Using Pythagoras' theorem the answer is equal to the square root of 2.

Using Pythagoras' theorem which says that the square on the hypotenuse (in this case the diagonal) is equal to the sum of the squares on the other two sides (which in the case of a square would be equal in length). so if the diagonal measured 10 units, the square on the diagonal would be 100 square units. And as this = 2*the squares on the other sides, the square on one side would be 100/2 = 50 square units. As a square has sides of equal length the square on one side is actually the area of the square. i.e. the area of a square with a diagonal of 10 units is 50 square units. or generically the area of a square with a diagonal of length 'x' = (x2)/2

Using Pythagoras: diagonal² = side² + side² = 2 × side² → side² = diagonal² ÷ 2 area = side² = diagonal² ÷ 2 = 14² ÷ 2 = 98 units²

Using Pythagoras: diagonal² = side² + side² = 2 × side² → side² = diagonal² ÷ 2 area = side² = diagonal² ÷ 2 → diagonal² = 2 × area → diagonal = √(2 × area) = √(2 × 36) = 6√2 ≈ 8.49

Using Pythagoras' theorem the diagonal is 16 times the square root of 2

Using Pythagoras: 322+362 = 2320 and the square root of this is the length of the diagonal

Some charts? Buildings Obtuse triangle - some of them are diagonal.

Using Pythagoras' theorem the length of the diagonal is 15 units

Cool question ! Answer - half it then cube it to prove it - an example for you if cube diagonal (not square diagonal) is 100, then using pythagoras theorm the square diagonal = 70.71068, If square the square diagonal = 70.71068, then using pythagoras theorm the side length = 50 therefore the volume = 50 ^ 3 = 25000 units works with any numbers

Not always, the diagonal can be figured out using the Pythagorean Theorem (a²+b²=c²). Where the diagonal is the hypotenuse (c). By rearranging the Pythagorean Theorem, you can see that the diagonal of a square is always 1.4 times the side of the square.