Triangle similarity selection

Choose a triangle that is similar to the given triangle. - ∆ TFC= t= 8 cm, f= 9 cm, c= 7 cm. :
∆ PKU= p= 45 cm, k= 35 cm, u= 40 cm.
∆ UPK= u= 40 cm, p= 45 cm, k= 35 cm.
∆ PUK= p= 45 cm, u= 40 cm, k= 35 cm.
∆ KPU= k= 35 cm, p= 45 cm, u= 40 cm.
∆ KUP= k= 35 cm, u= 40 cm, p= 45 cm

Final Answer:

x = UPK

Step-by-step explanation:

$$\begin{gathered} t=8\text{cm} \\ f=9\text{cm} \\ c=7\text{cm} \\ k=35\text{cm} \\ u=40\text{cm} \\ p=45\text{cm} \\ c<t<f \\ k<u<p \\ {r}_1=k/c=35/7=5 \\ {r}_2=u/t=40/8=5 \\ {r}_3=p/f=45/9=5 \\ {r}_1=r_2=r_3 \\ \Delta UFC->\Delta JUP \\ \Delta TFC->\Delta UPK \\ x=UPK \end{gathered}$$

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