Question

Geometry question: if triangle VSY is isosceles and its perimeter is less than 45, which side is true base? (Reference picture)

Answer 1

Step-by-step explanation:

Case 1

Let SV and SY be the two equal sides.

`\begin{gathered} SV\cong SY\implies2x-8=10 \\ 2x=10+8 \\ 2x=18 \\ x=9 \end{gathered}`

This will make the length of the third side:

`VY=x+7=9+7=16`

In this scenario, the perimeter of the triangle will be:

`\text{Perimeter}=10+10+16=36<45`

Case 2

If VY and SY are the two equal sides:

`\begin{gathered} x+7=2x-8 \\ \implies2x-x=7+8 \\ \implies x=15 \end{gathered}`

However, in this case, the perimeter will be: 22+22+10=54

Case 3

If SV and VY are the two equal sides:

`x+7=10\implies x=3`

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.