2015 r 26 triangle abc is similar to triangle def the side...

Triangle ABC is similar to Triangle DEF. The side lengths of triangle ABC are given by the expressions: AB = x2, BC = 6x – 4, and AC = 4x. If the linear scale factor from ABC to DEF is 1:3, which of the following expressions would represent the perimeter of triangle DEF? (a) 3x^2 + 10x – 4 (b) 3x^2 + 12x + 18 (c) 3x^2 + 30x – 12 (d) X^2 + 18x – 12

Transcript

00:01 This problem says that triangle abc is similar to triangle def, and the side lengths of triangle abc are given with the expressions, x squared for ab, 6x minus 4 for bc, and 4x for ac.

00:11 And if the linear scale factor from abc to def is 1 to 3, which of the following expressions would represent the perimeter of triangle def? so to remind us what perimeter is, perimeter is just adding up all of our sides of our shape and figuring out the total length all the way around our shape.

00:27 But to be able to figure out the perimeter of triangle d -e -f, based off of measurements for triangle a -b -c, we need to apply that linear scale factor to get from the links from a, b, and c, to d, and f.

00:38 So, multiplying all of these by three will give us our new side links, and that will be 3x squared, and then 3 would distribute to 6x and minus 4, so that would give us 18x minus 12, and then 4x times 3 would give us 12x.

00:55 So to get that perimeter of this triangle def, we have the sides that would represent the sides of triangle def now.

01:03 So we just need to add them all up.

01:05 So 3x squared plus 18x minus 12, plus 12, and combine our like terms.

01:11 We only have 1x squared, so that will stay.

01:14 And then we have 1x terms, so that will stay as well, plus 18.

01:18 Or excuse me, it should be plus 12x.

01:20 Let me fix that, because that is 4x times 3.

01:24 That should be 12x, not just 12.

01:26 So we have now 3x squared plus 18x...