Question

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.

Answer 1

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