Question

δstu is an equilateral triangle. if st = 2x - 1, su = 5x - 37, and tu = x + 11, solve for x.

Explanation:

Step1: Use property of equilateral triangle

In an equilateral triangle, all sides are equal. So we can set up an equation using two - side lengths. Let's set $ST = TU$.
$2x - 1=x + 11$

Step2: Solve for x

Subtract $x$ from both sides of the equation:
$2x-x-1=x - x+11$
$x - 1=11$
Then add 1 to both sides:
$x-1 + 1=11 + 1$
$x = 12$
We can also check by setting $ST = SU$ or $SU=TU$. Let's check with $ST = SU$.
When $x = 12$, $ST=2x-1=2\times12 - 1=24 - 1 = 23$, $SU=5x-37=5\times12-37=60 - 37 = 23$, $TU=x + 11=12+11 = 23$

Answer:

$12$