A triangle has side lengths of (1.2u+1.8v)(1.2u+1.8v) centimeters, (6.5u+8.7w)(6.5u+8.7w) centimeters, and (5.8w-6.9v)(5.8w−6.9v) centimeters. Which expression represents the perimeter, in centimeters, of the triangle? 13.5uw+3.6vw13.5uw+3.6vw 7.7u+1.8w+7.6v7.7u+1.8w+7.6v -1.1vw+15.2uw+3uv−1.1vw+15.2uw+3uv 14.5w-5.1v+7.7u14.5w−5.1v+7.7u

7.7u - 5.1v + 14.5w

Step-by-step explanation:

Given length:

Side A = (1.2u+1.8v) centimeters,

Side B = (6.5u+8.7w) centimeters

Side C = (5.8w-6.9v) centimeters

Perimeter of a triangle = side A + side B + side C

= (1.2u+1.8v) + (6.5u+8.7w) + (5.8w-6.9v)

= 1.2u + 1.8v + 6.5u + 8.7w + 5.8w - 6.9v

Collect like terms

= 1.2u + 6.5u + 1.8v - 6.9v + 8.7w + 5.8w

= 7.7u - 5.1v + 14.5w

Therefore, the perimeter of the triangle is 7.7u - 5.1v + 14.5w

rectangle: 9 1/8 x 4 1/9 = 37 37/72in

parallelogram: b times h= 10.3 x 6.2 = 63.86

trapezoid: a+b/2 times h= 42.5

volume of prism: l times w times h= 36

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.