Question

If RX = 4 and XS = 9, then XT =6
6.5
√13
18

Answer 1

Please teach me how to solve these not just the answer!! Thanks!

Answer 2

ook wht u need to calculate??? and u see there are two right angled triangles ...so we gonna use Pythagores theorem

Answer 3

ok

Answer 4

so which side length u need to calculate ?? @Natasha18

Answer 5

ooh sorry the question didn't come out right

Answer 6

XT doesnt = 6, 6 is just one of the options

Answer 7

we want to find XT

Answer 8

OK, they are right triangles, so the Pythagorean Theorem is going to work. That's a pretty common one, do you know it?

Answer 9

a^2 + b^2 = c^2

Answer 10

Yep, hang on a second.

@rishavraj may I jump in? I've got a slow connection so I can't see if you are still here?

Answer 11

lol for sure....was stuck on my work :P

Answer 12

@Natasha18
This is a bit trick to set up, so stop me anytime with a question.

The difficulty is, we have three missing sides. And the diagram is untrustworthy.

Answer 13

yeah.. they're similar triangles right?

Answer 14

@Natasha18
see lemme simplify it
here u got 3 right angle triangles ..... cool with it ???
triangle RST , triangle RXT and triangle XST
so for traingle RST ...we have RS = 13
\[RS^2 = RT^2 + ST^2 \]

Answer 15

uuummm i only see two right triangles

Answer 16

TXS and TXR

Answer 17

@Natasha18
wht about RST ??

Answer 18

it isn't a right triangle

Answer 19

wait oh nvm it is lol

Answer 20

http://prntscr.com/bhm0vf

Answer 21

That little square in the corner of says that there is a right angle at <RTS. That should make RTS a right triangle. Is there something that makes you think otherwise?

Answer 22

no i just wasn't looking closely enough

Answer 23

so in traingle RST
\[13^2 = (TS)^2 + (TR)^2\]
@Natasha18 u get tht??

Answer 24

yeah

Answer 25

Guys, shorter way! Shorter way! @Natasha was right about similar triangles!

Answer 26

@mjdennis yeah i think i was supposed to solve it using knowledge of similar triangles

Answer 27

oops my bad @Natasha18

Answer 28

dw:1466184169904:dw|

Answer 29

for some reason your drawing isnt loading

Answer 30

Lost the drawing. One sec. There are three right triangles, and because XT is perpendicular to the base, all three are similar. (That line XT is an altitude, right?)
So if they are similar, the sides are proportional.

So, @Natasha , need you to match sides for me:

Answer 31

Ratio RX/XT on smallest triangle is going to match what ration of sides on the medium-sized triangle TXS ?

Answer 32

ok well ST = TX, TS= TR=SR , RX= SX ... is that all of them?

Answer 33

TX to SX

Answer 34

Maybe I read it wrong, but I get RX~TX~RT for the short sides,
XT~XS~TS for the long side and RT~TS~RS for the hypotenuses.

Answer 35

ok yeah i see that... im just horrible with similar triangles

Answer 36

No, you nailed the ratio. (I was horrible once, too).

So RX/XT = TX/SX

TX is really XT, and you know RX and SX. Can you 'bring it home'?

Answer 37

36 = tx^2 so the answer is 6

Answer 38

Brava, well done! @rishavraj was on the way to an excellent solution with a quadratic equation, too.

Answer 39

well im glad i did it this way... i hate quadratic equations XD