Similar triangles?

Question

in triangle RST, KA parallels SR. if TA=8, KA=12, AR=4, then
AR=________

A. 3 B. 6 C. 9 D. 12 E. 18

Answer 1

I assume you're looking for SR, not AR, which is given in the problems. Because KA is parallel to SR, it divides the triangle into a similar one. Therefore the proportion of sides is constant. So, since TR = TA+AR = 12, we have TA / TR = KA / SR. Then 8 / 12 = 12 / SR, so SR = 18.

Steve

Answer 2

E. 18

First, I will assume KA is "in" triangle RST since that is certainly possible and gives an obvious value to desire. I mention the obvious value to desire because you gave AR=4 in the information and it seems likely you don't really want that for the answer! Not least because no answer is 4...

Secondy, I place K and A to "follow" S and R. In other words, K is on TS and A is on TR. Since KA is parallel to SR, that makes triangle AKT similar to RST so the sides are in proportion to one their similar mates. You give TA and AK in AKT and by giving AR we also have TR as 8 + 4 = 12. So the obvious answer needed is the length of side SR, not AR. AK is to AT as SR is to RT: 12:8::SR:12 and rearranging however you prefer, cross-multiplying perhaps, we have 12 / 8 * 12 = 18. So answer E is correct.

Answer 3

6

Answer 4

You have already given the length of AR, so I am assuming, albeit warily, that you mistyped AR instead of TR, since A and T both lie on the same line segment. If that is the case, then TR = 12.

Answer 5

Well, the way you've written the problem AR = 4 QED. It's part of your given information. Try a rewrite.

Answer 6

Technically the answer is not listed because you said in the given, that AR=4, find AR. However, if you intended to say find RS you would set up the following proportion.

TA/AK=TR/RS
8/12=(4+8)/x
2/3=12/x
2x=36
x=18

Choice (E)

P.S. Please watch your wording next time! :-)

Answer 7

Hi,

You need to revise your question. It asks you to solve for AR, but AR is listed in your given info.