The measures of two sides of a triangle are (2 + 3) and (5 − 2). If the perimeter of the triangle is (12 + 5), what is the measure of the third side?

9

Step-by-step explanation:

First side: (2+3)=5

Second side: (5-2)=3

Perimeter: (12+5)=17

Take perimeter and minus the first and second side

17-5-3=9//

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.

the correct answer is the second option