Find the perimeter of a square to the nearest tenth if the length of its diagonal is 16 millimeters
Diagonal = 16 = sqrt(2x^2)
x = 8*sqrt(2) mm
Perimeter = 4*x = ?
To find the perimeter of a square, you need to know the length of one side.
In a square, the diagonal bisects the right angles of the square, creating 45-45-90 degree triangles on each half of the square.
In a 45-45-90 degree triangle, the ratio of the sides is 1:1:√2. This means that the length of the diagonal (√2) is equal to the length of one side of the square.
Given that the length of the diagonal is 16 millimeters, we know that one side of the square is (√2) * 16 millimeters.
Calculating (√2) * 16 = 22.62741699796 millimeters.
However, we are asked for the perimeter to the nearest tenth. To do this, round the calculated value to the nearest tenth:
Rounded value = 22.6 millimeters.
The perimeter of the square is 4 times the length of the side, so the perimeter is:
4 * 22.6 = 90.4 millimeters (rounded to the nearest tenth).
Therefore, the perimeter of the square, rounded to the nearest tenth, is 90.4 millimeters.