Answer :
Answer:
[tex]QT = 10[/tex]
Step-by-step explanation:
Given
[tex]Perimeter = 55[/tex]
See attachment for triangle
The perimeter is calculated as:
[tex]Perimeter = QR + RS + QS[/tex]
This gives:
[tex]55 = 3x + 18 + 2x +12[/tex]
Collect like terms
[tex]3x + 2x = 55 - 18 - 12[/tex]
[tex]5x = 25[/tex]
[tex]x = 5[/tex]
From the attachment:
[tex]QT = 2x[/tex]
[tex]QT = 2 * 5[/tex]
[tex]QT = 10[/tex]
Triangle QRS has a perimeter of 55. If RT bisects angle R, then the length of QT is 10 and this can be determined by using the formula of the perimeter of a triangle.
Given :
- Triangle QRS has a perimeter of 55.
- RT bisects angle R.
- QS = 2x +12
- QR = 3x
- RS = 18
The perimeter of the triangle QRS is given by:
Perimeter = QR + RS + QS
55 = QR + RS + QS
Now, put the values of sides QR, RS, and QS in the above equation.
55 = 3x + 18 + 2x + 12
55 = 5x + 30
25 = 5x
x = 5
Now, the length of the QT is given by:
QT = 2x
QT = 10
For more information, refer to the link given below:
https://brainly.com/question/919810