Q: The diagonal of a square has the length of 10 square root of 2 ft what is the length of the square?

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The diagonal is 15.620 meters.

Pythagoras' theorem shows the side you are looking for, the hypotenuse of the right angles triangle is the root of the sum of the other two sides, so it is root(10 squared+ 10 squared)= root(200)=10*root2 or 14.1421356 inches

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

If the circle is inscribed in the square, the side length of the square is the same as the diameter of the circle which is twice its radius: → area_square = (2 × 5 in)² = 10² sq in = 100 sq in If the circle circumscribes the square, the diagonal of the square is the same as the diameter of the circle; Using Pythagoras the length of the side of the square can be calculated: → diagonal = 2 × 5 in = 10 in → side² + side² = diagonal² → 2 × side² = diagonal² → side² = diagonal² / 2 → side = diagonal / √2 → side = 10 in / √2 → area _square = (10 in / √2)² = 100 sq in / 2 = 50 sq in.

The area of one side is square root (10).

Related questions

If the area of a square is 100, then its side length is 10. If we draw in a diagonal, then we know by the Pythagorean formula that the diagonal's length is sqrt(10^2 + 10^2) = sqrt(200) = 10*sqrt(2).The square root of 2 is approximately 1.414, so the diagonal's length is approximately 10*1.414 =14.14* The diagonal of any square is the side length times (sq rt 2).

The diagonal = the square root of (6 squared + 8 squared) 6 squared+8squared = 100 the square root of 100 = 10 so the length of the diagonal is 10. The above used Pythagoras' theorem which says the square on the diagonal is equal to the sum of the squares on the other two sides.

Using Pythagoras' theorem it is 10 times the square root of 2 which is about 14 feet

10' x 16' is not a square but a rectangle and the diagonal is square root of (10^2 + 16^2) = square root of (100 + 256) = square root of 356 which is 18.867 feet

The diagonal is 15.620 meters.

Pythagoras' theorem shows the side you are looking for, the hypotenuse of the right angles triangle is the root of the sum of the other two sides, so it is root(10 squared+ 10 squared)= root(200)=10*root2 or 14.1421356 inches

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

If the circle is inscribed in the square, the side length of the square is the same as the diameter of the circle which is twice its radius: → area_square = (2 × 5 in)² = 10² sq in = 100 sq in If the circle circumscribes the square, the diagonal of the square is the same as the diameter of the circle; Using Pythagoras the length of the side of the square can be calculated: → diagonal = 2 × 5 in = 10 in → side² + side² = diagonal² → 2 × side² = diagonal² → side² = diagonal² / 2 → side = diagonal / √2 → side = 10 in / √2 → area _square = (10 in / √2)² = 100 sq in / 2 = 50 sq in.

Using Pythagoras' theorem it is 10 times square root of 2 or about 14.142 to 3 decimal places

14.142 cm (rounded)

Approximately 10 inches.

The best way to do this would be to use the Pythagorean Theorem, but in reverse. So let's say the diagonal is 10, and the width is 8. You would do (10^2) / (8^2). This equals 36. The square root of 36 is 6. So your answer would be 6 for the length. Hope this answer helps!