Question

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

x =
fh =
hg =

Explanation:

Step1: Set up equation

Since $\triangle FGH$ is equilateral, all sides are equal. So we set $6x + 1=3x + 10$.
$6x+1 = 3x + 10$

Step2: Solve for $x$

Subtract $3x$ from both sides and subtract 1 from both sides.
$6x-3x=10 - 1$
$3x=9$
$x = 3$

Step3: Find length of $FH$

Substitute $x = 3$ into the expression for $FH$ which is $6x+1$.
$FH=6\times3 + 1=18 + 1=19$

Step4: Find length of $HG$

Substitute $x = 3$ into the expression for $HG$ which is $9x - 8$.
$HG=9\times3-8=27 - 8=19$

Answer:

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