Question

1. find the length of each side if △fgh is an equilateral triangle

x =
fh =
hg =
fg =

Explanation:

Step1: Set two - side lengths equal

Since it's an equilateral triangle, we can set $6x + 1=3x + 10$.
$6x+1 = 3x + 10$
$6x-3x=10 - 1$
$3x=9$
$x = 3$

Step2: Check with another pair

We can also check by setting $6x + 1=9x - 8$.
$6x+1=9x - 8$
$9x-6x=1 + 8$
$3x=9$
$x = 3$

Step3: Find the side - length

Substitute $x = 3$ into any side - length expression. Let's use $6x + 1$.
When $x = 3$, $6x+1=6\times3+1=18 + 1=19$.
Since it's an equilateral triangle, $FH=HG=FG = 19$.

Answer:

$x = 3$
$FH=19$
$HG=19$
$FG=19$