Selection 4

Selection triangle, which is similar to the given triangle RTG.
∆ RTG, r= 24 dm, t = 28 dm, g= 30 dm.
∆ SHV= 6 dm, h= 7.5 dm, v= 7 dm
∆ VSH= v= 7 dm, s= 6 dm, h= 7.5 dm
∆ HVS= h= 7.5 dm, v= 7 dm, s = 6 dm.
∆ VHS= v= 7 dm, h = 7.5 dm, s= 6 dm.
∆ HSV= h= 7.5 dm, s= 6 dm, v= 7 dm.
∆ SVH= s= 6 dm, v= 7 dm, h= 7.5 dm.

Final Answer:

x = SVH

Step-by-step explanation:

$$\begin{gathered} r=24\text{dm} \\ t=28\text{dm} \\ g=30\text{dm} \\ s=6\text{dm} \\ h=7.5\text{dm} \\ v=7\text{dm} \\ r<t<g\dots \Delta RTG \\ s<v<h\dots \Delta SVH \\ {r}_1=r/s=24/6=4 \\ {r}_2=t/v=28/7=4 \\ {r}_3=g/h=30/7.5=4 \\ {r}_1=r_2=r_3 \\ \Delta SVH \\ x=SVH \end{gathered}$$

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