Question

find eg.
e
2x + 11
d
g
14x - 37
f

Explanation:

Step1: Set equal sides

Since the two - triangles formed by the line $DG$ have equal hypotenuses (the tick - marks indicate congruent sides), we set up the equation $2x + 11=14x−37$.
$2x + 11=14x−37$

Step2: Solve for $x$

Subtract $2x$ from both sides:
$11 = 14x-2x - 37$
$11=12x - 37$
Add 37 to both sides:
$11 + 37=12x$
$48 = 12x$
Divide both sides by 12:
$x=\frac{48}{12}=4$

Step3: Find $EG$

Substitute $x = 4$ into the expression for $EG$ which is $2x + 11$.
$EG=2\times4 + 11$
$EG=8 + 11$
$EG = 19$

Answer:

$19$