Answer:
Explanation:
Case 1
Let SV and SY be the two equal sides.
[tex]\begin{gathered} SV\cong SY\implies2x-8=10 \\ 2x=10+8 \\ 2x=18 \\ x=9 \end{gathered}[/tex]
This will make the length of the third side:
[tex]VY=x+7=9+7=16[/tex]
In this scenario, the perimeter of the triangle will be:
[tex]\text{Perimeter}=10+10+16=36<45[/tex]
Case 2
If VY and SY are the two equal sides:
[tex]\begin{gathered} x+7=2x-8 \\ \implies2x-x=7+8 \\ \implies x=15 \end{gathered}[/tex]
However, in this case, the perimeter will be: 22+22+10=54
Case 3
If SV and VY are the two equal sides:
[tex]x+7=10\implies x=3[/tex]
However, this scenario will make the length of SY negative (-2) which is not possible.
Thus, the only possible case is Case 1.
VY will be the base for the perimeter to be less than 45 units.
