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



and i can try to describe were each letter is Q is at the very top wile S is bottem right R is bottem left U is bottem middle and T is top middle

Answer 1

Interpreting your description: the big triangle QSR is split by the segment TU into two smaller triangles QT R (left) and TS U (right). The two small triangles are marked with the same angle (54°) and they also share the angle at T where the cut meets the top side, so the two small triangles are similar by AA. The base of the left small triangle is 3 and the base of the right small triangle is 6, so the similarity ratio is 3:6 = 1:2.

From the similarity,
QT : TS = 3 : 6 = 1 : 2,
so QT = TS/2. You said TS = 7, hence QT = 7/2 = 3.5.

The whole top side QS = QT + TS = 3.5 + 7 = 10.5 = 21/2.

Therefore x = 10.5 (or 21/2).

If I misread the figure, upload or sketch the diagram and I’ll re-check.