Question

Solve for .x. The triangles in each pair are similar.3)4) FGH-QRS

Answer 1

Due the triangles in each pair are similar, the ratio between the corresponding sides is constant and equal for the three pair of sides.

For problem 1, we have:

`\begin{gathered} (PF)/(PQ)=(PG)/(PR) \\ (2x-9)/(27)=(9)/(27) \\ 2x-9=9 \\ 2x=9+9 \\ x=(18)/(2) \\ x=9 \end{gathered}`

So, x = 9.

For problem 3, we have:

`\begin{gathered} (SR)/(SF)=(SQ)/(SE) \\ (11x-13)/(20)=(78)/(12) \\ 11x-13=(13)/(2)\cdot20 \\ 11x=130+13 \\ x=(143)/(11)=13 \end{gathered}`

So, x = 13.

For problem 4, we have:

`\begin{gathered} (FG)/(RQ)=(GH)/(RS) \\ (8x+7)/(9)=(84)/(12) \\ 8x+7=7\cdot9 \\ 8x=63-7 \\ x=(56)/(8) \\ x=7 \end{gathered}`

So, x = 7.