Answer:
The value of x = 12 and the measure of each side is 23 units.
Step-by-step explanation:
Given: STU is an equilateral triangle.
ST = 2x -1
SU = 5x - 37
TU = x + 11
Now, as Δ STU is an equilateral triangle, hence all the sides of the triangle are equal.
⇒ ST = SU = TU
or, 2x -1 = 5x - 37 = x + 11
Considering : 2x -1 = 5x - 37 , we get
-1 + 37 = 5x - 2x
or 3x = 36
or, x = 12
Considering : 5x - 37 = x + 11 , we get
5x -x = 11 + 37
or, 4x = 48 or, x = 12
Considering : x + 11 = 2x -1
or, 2x - 1 = x + 11
or, x = 12
hence, in all the cases value of x = 12
ST = 2x -1 = 2(12) -1 = 23 units
SU = 5x - 37= 5(12) -1 = 23 units
TU = x + 11 = 12 = 11 = 23 units
