Answer:
<em>Option B; EF = ( About ) 4.47 units, Perimeter of Δ EFG = ( About ) 12.94 units</em>
Step-by-step explanation:
If we were to consider the height of this triangle EFG, it would be 4 units of length, supposedly splitting base GF into two ≅ parts, each 2 units of length. First let us name the point drawn to base GF ⇒ point H, so that the height of Δ EFG ⇒ EH. Now as EH splits GF into two ≅ parts, by Converse to Coincidence Theorem, Δ EFG ⇒ Isosceles Δ;
EH and FH are legs of a right triangle EFH, so that Pythagorean Theorem can be applied to solve for the length of EF and EG, knowing that as Δ EFG ⇒ Isosceles Δ, EF ≅ EG;
( EH )^2 + ( FH )^2 = ( EF )^2,
( 4 )^2 + ( 2 )^2 = ( EF )^2 ⇒ take square of 4 & 2,
16 + 4 = ( EF )^2 ⇒ combine like terms,
( EF )^2 = 20 ⇒ take square root on either side to solve for EF,
EF = √ 20 =<em> ( About ) 4.47 units</em> = EG,
Perimeter of Δ EFG = EF + GF + EG = 4.47 + 4 + 4.47 = <em>( About ) 12.94 units,</em>
<em>Solution; Option B</em>
