1. If the diagonal of a square is 22 ft, find the perimeter of the square. Give in simplest radical form where possible?
2. If the perimeter of an isosceles right triangle is (16+8\sqrt2)cm, what is the length of the hypotenuse? Give in simplest radical form where possible.
1. Each side of the square = 22/sqrt (2)
So.....the perimeter = 4 * 22/sqrt (2) = 88/sqrt (2) = 88 sqrt (2) / 2 = 44 sqrt (2)
2. One of the sides of the triangle = (1/sqrt (2) ) ( 16 + 8/sqrt (2) ) = 16/sqrt (2) + 8/2 =
16 sqrt (2) / 2 + 4 = 8sqrt (2) + 4
So the perimeter = 2 [ 8sqrt (2) + 4 ] + 16 + 8/sqrt (2) =
16sqrt (2) + 8 + 16 + 8sqrt (2) / 2 =
16sqrt (2) + 8 + 16 + 4sqrt (2) =
24 + 20 sqrt (2)