In 16 by 12 rectangle , what is the perimeter of the triangle formed by two sides of the rectangle and the diagonal.

Let the length be L= 16 and the width be w =
12.

Since the sides of a rectangle are perpendicular to
each other, the triangle formed by two sides of rectangle and the diagonal is a right
angle triangle.

The hypotenuse of the right angle triangle
is the diagonal of rectangle and the legs are the length and the width of
rectangle.

Let D be the diagonal of rectangle and the
hypotenuse of right angle triangle.

To calculate the
perimeter of this triangle, we need to know all the lengths of the sides, but, for the
moment, we only know the lengths of the legs.

We'll
determine the length of hypotenuse using the Pythagorean
theorem:

D^2 = L^2 + w^2

D^2 =
16^2 + 12^4

D^2 = 256 +
144

D^2 = 400

D =
20

Since the length of a side cannot be negative, we'll
keep only the positive value of D.

We can calculate now the
perimeter of triangle:

P = L + D +
w

P = 16 + 20 + 12

P =
48

The requested perimeter of triangle formed
by two sides of rectangle and the diagonal of rectangle is  p  = 48
units.