It's basically mandatory to memorize the three most common special triangles: the 3-4-5 triangle, the 30-60-90 triangle, and the right isosceles. They appear constantly. Sometimes they appear in my sleep. Anyway, we recognize that the upper triangle in the given rectangle is a 3-4-5 triangle that's been expanded by a factor of 2 to get a 6-8-10 triangle. (We know it's a right triangle because a rectangle must have right angles at its corners.) The missing side on the top of the rectangle must therefore be 8. Since we know that halfway around the rectangle is 6 + 8, giving us 14, the full perimeter must be 14x2, or 28, giving us answer choice C.
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We see that we have a 6-8-10 right triangle, so the length of the rectangle must be 8.

Thus, the perimeter is 6 x 2 + 8 x 2 = 12 + 16 = 28.

Answer: C
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