For which of the following sets of three squares does the Pythagorean relationship
hold? Show your work.
a) 10 cm2, 4 cm?, 14 cm
b) 3 cm², 12 cm², 16 cm
c) 5 cm², 27 cm², 22 cm?
d) 21 cm², 2 cm?, 19 cm

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

answer: was that a question or answer?

step-by-step explanation:

7

step-by-step explanation:

the answer would be 7