Answer:
Option B is correct
the perimeter is, [tex]24+8\sqrt{3}[/tex] units
Step-by-step explanation:
Let H represents the Hypotenuse side, S represents the shorter side and L represents the side of the longer.
In a 30-60-90 triangle,
The hypotenuse is twice the length of the shorter leg,
and the length of the longer leg is [tex]\sqrt{3}[/tex] times the length of the shorter leg.
As per the statement:
The length of the hypotenuse of a 30 -60 -90 triangle is 16
⇒[tex]\text{Length of hypotenuse side} = 16[/tex] units.
then by definition of 30-60-90 triangle.
⇒[tex]H = 2S[/tex]
⇒[tex]16 = 2S[/tex]
⇒[tex]8 = S[/tex]
or
S = 8 units
Also. length of the longer leg is [tex]\sqrt{3}[/tex] times the length of the shorter leg
⇒[tex]L = \sqrt{3} \cdot 8[/tex]
⇒[tex]L = 8\sqrt{3}[/tex] units
Perimeter(P) of a 30-60-90 triangle is sum of all the three sides i.e,
[tex]P = L+S+H = 8\sqrt{3}+8+16 = 8\sqrt{3}+24[/tex]
Therefore, the perimeter is, [tex]24+8\sqrt{3}[/tex] units
