triangle STU is an equilateral triangle. If ST is one less than twice x, SU is 37 less than five times x, and TU is 11 more than x, find x and the measure of each.

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