Because the garden is square, we have a very simple problem.
The area of any square is the simply the product of any two sides. Contrariwise, to find the length of any side, you'd find the square root of the area. The area is 128 m² and so the length of any one side would be the square root of 128, or 8 times the square root of 2.
From there, if you were to take any two adjacent sides and connect the free corners by a line, that would be the same as the diagonal of the original square. You could find its length by applying the Pythagorean theorem (side 1)² + (side2)² = (diagonal)², chiefly because the angle opposite the diagonal is a right angle.
So ...
(diagonal)² = (8 root 2)² + (8 root 2)²
(diagonal)² = 128 + 128
(diagonal)² = 256
diagonal = 16
So, this particular square garden has a diagonal of 16 meters.
The area of any square is the simply the product of any two sides. Contrariwise, to find the length of any side, you'd find the square root of the area. The area is 128 m² and so the length of any one side would be the square root of 128, or 8 times the square root of 2.
From there, if you were to take any two adjacent sides and connect the free corners by a line, that would be the same as the diagonal of the original square. You could find its length by applying the Pythagorean theorem (side 1)² + (side2)² = (diagonal)², chiefly because the angle opposite the diagonal is a right angle.
So ...
(diagonal)² = (8 root 2)² + (8 root 2)²
(diagonal)² = 128 + 128
(diagonal)² = 256
diagonal = 16
So, this particular square garden has a diagonal of 16 meters.