About 11.31 units.
A diagonal of a square measures: Side X sqrt(2).Approximately (8 cm) X (1.414) = 11.312 cm
Using Pythagoras' theorem: 8 times the square root of 2 which is about 11,3137085 cm
Designate the length by L. From the Pythagorean theorem, the length of the diagonal of a square, which divides the square into two right triangles, each with sides L (and the diagonal as hypotenuse to each right triangle), is square root of 2L2 = 4 (from the problem statement). Squaring both sides separately yields 2L2 = 16 or L = square root of 8 = 2 (square root of 2).
A square with a side length of 8 cm has an area of 64 cm2
The sides of squares are all equal. Let the side of the square be x. Area of square is therefore x^2. x^2 = 64 x = sq. rt 64 x = 8 or -8 (rej. because length cant be -ve) The length is, therefore, 8.
8*sqrt(2) The diagonal of the square would be the hypotenuse of the right triangle formed by two of the sides of the square.
A diagonal of a square measures: Side X sqrt(2).Approximately (8 cm) X (1.414) = 11.312 cm
The square root of 128, approxiametaly 11.313
About 5.656854249 cm using Pythagoras' theorem: 2x2 = 64
11.3137085 units
a≈2.83cm The sides are the square root of 8 cm, approximately 2.8284 cm
Using Pythagoras' theorem: 8 times the square root of 2 which is about 11,3137085 cm
Area = 64 cm2 so length of side = 8cm Then, by Pythagoras, length of diagonal = sqrt[82 + 82] = 8*sqrt(2) = 11.3137 cm (to 4 dp)
Designate the length by L. From the Pythagorean theorem, the length of the diagonal of a square, which divides the square into two right triangles, each with sides L (and the diagonal as hypotenuse to each right triangle), is square root of 2L2 = 4 (from the problem statement). Squaring both sides separately yields 2L2 = 16 or L = square root of 8 = 2 (square root of 2).
Diagonal = sqrt (twice the square of a side) eg: square of side 8 units, d = sqrt(2 x 64) = sqrt 128 = 11.3137
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.
Let 'a' and 'b' be the length of one side and diagonal of a square. Pythagorus's theorem as applied to a square: a^2 + a^2 = b^2. Substituting a = 2 into the equation, we have b^2 = 2^2 + 2^2 = 8. b = sqrt(8) = 2 * sqrt(2). Q.E.D. ===========================