Question

I need to show work..

Answer 1

Step-by-step explanation:

Since the two sides of the triangle are equal and (it appears) the angle $D$ is bisected by $DG$, then we can say that $EG$ and $GF$ are equivalent.

Knowing this, we can set the two lines equal to each other and solve for $x$:

$2x + 11 = 14x - 37$

$2x - 14x = -37 - 11$

$-12x = -48$

$x = 4$

Since we need to find $EG$, we need to plug in $x = 4$ into its equation:

$2x + 11$

$2(4) + 11$

$8 + 11$

$19$

Answer 2

Answer:

$2x + 11 = 14x - 37 \\11 + 37 = 14x - 2x \\ 48 = 12x \\ \frac{48}{12} = \frac{12x}{12} \\ 4 = x$

now let's find the value of EG

$eg = 2x + 11 \\ x = 4 \\ \\ 2x + 11 \\ 2 \times 4 + 11 \\ 8 + 11 \\ = 19$