Question

Solve for x. Figures are not necessarily drawn to scale.

This is a tri that is cut in the middle with 2 parts connected at the center the origanl tri was QSR now its split form is QTUR and TSU or QTUSR

q top R bottom left s bottom right and down the middle of it all is line T to U spliting it in half one half witch is TSU has a degree of 54 and 7 top 6 bottem wile QTUR is same degree but 3 bottom no top number and above it all that is a line indicating the top side is equal to X witch is the line QTS were T to S holds 7


i cant show the picture per say but try to give some number with this info oh and on the 1 side there is also no number but if we remove the cut the top is going to be 7 + _ = X bottem is 9 and side still no number

Answer 1

I can help, but I need a clearer picture of how the points and numbers are placed. Your description is a bit hard to parse into a geometric diagram. Can you confirm (or correct) the following questions so I know exactly what to solve?

1. Which three points are the vertices of the original big triangle? (You wrote Q top, R bottom-left, S bottom-right — is that correct?)
2. Where exactly are T and U located?
- Is the "cut down the middle" the segment from Q to the base RS meeting it at a point U? Or is it a vertical segment TU with T on QS and U on QR? Or something else?
3. Which segments/angles correspond to the numbers you gave?
- Which segment is length 7? Which is 6? Which is 3? Which is 9?
- Which angle is 54° and at which vertex?
4. Which segment is labeled X (what is X supposed to be the length of)?
5. Is the cut an angle bisector, a median, or just some arbitrary segment? (You wrote “split in half” — do you mean it splits the triangle into two triangles of equal area, or it is the angle bisector, or the perpendicular bisector, etc.?)

If it’s easiest, you can upload a quick photo, or draw an ASCII sketch like:

Q
|\
| \
| \
T \
| \
U-----S
\ |
\ |
\ |
\ |
R

and put the numbers next to the segments/angles.

---

While you prepare that, here are the common ways this kind of problem is solved depending on what the cut is:

A. If the cut from Q to the base RS is an angle bisector (meets RS at U):
- Use the Angle Bisector Theorem: RU / US = RQ / QS.
Example: if RU = 6 and US = 3, then RQ / QS = 6 / 3 = 2, so RQ = 2·QS.
If you also know one piece of QS (say TS = 7) you still need another relation (a side length or an angle) to compute absolute lengths.

B. If the cut is a median (meets RS at its midpoint):
- Then RU = US and you can use that equality in combination with other side data.

C. If you know an angle and an opposite side in one of the small triangles:
- You can use the Law of Sines or Law of Cosines to relate the sides and find X.

Example worked small scenario (to show method):
- Suppose RU = 6, US = 3 (so RS = 9). Suppose QU is the angle bisector. Suppose TS (part of QS) = 7 and we want QS = X.
From angle-bisector: RQ / QS = RU / US = 6/3 = 2, so RQ = 2·QS.
If we also know RQ = some numeric value (say 14) we can solve QS = 7 = X. But without one more numeric relation, X is not determined.

So: I can give the exact numeric answer once you confirm the precise positions of the points and which numbers label which segments/angles. If you can re-draw or upload a photo, I’ll finish the solution quickly.