What's the answer?
a
b
c
d
nothing else

Special triangles tell us that: 45-45-90 angles mean side ratios of 1-1-sqrt2, 30-60-90 angles have side ratios of 1-sqrt3-2.
Beginning from the upper-left corner and working clockwise:
The first side is a 45-45-90 triangle with legs of 24 in, so the hypotenuse is 24sqrt2.
The upper-right triangle is a 30-60-90, and the side opposite 30 degrees has length 24, so the hypotenuse is twice that, which is 48.
The right side is just x = 24.
The remaining three sides are identical to the first three (one from a 45-45-90 hypotenuse, another a 30-60-90 hypotenuse, and the last equal to x).
So the total perimeter is 24sqrt2 + 48 + 24 + 24sqrt2 + 48 + 24 = 144 + 48sqrt2 inches. This is choice D.