Respuesta :

Dead3ill

Answer:

x = 7

y = 12

PQ = QR = 29

Step-by-step explanation:

In ΔPSR , PS = SR (given)

[tex]=> 4x+4=7x-17\\=> 7x-4x=17+4\\=>3x=21\\=>x=\frac{21}{3}=7[/tex]

In ΔPQR , QT is perpendicular bisector of PR. So , PT = RT . As ΔPQR has a perpendicular bisector , it is an isosceles triangle.

So,

,[tex]PQ = RQ\\=>5y-31=2y+5\\=>5y-2y=31+5\\=>3y=36\\=>y=\frac{36}{3} =12[/tex]

akposevictor

Applying the Pythagorean Theorem and the definition of perpendicular bisector, the values of x and y, as well as the measures of each segment in the image are:

  • x = 7
  • y = 12
  • QT = 22.7
  • PQ = 29
  • PT = TR = 18
  • QR= 29
  • PS = 32
  • SR = 32

Given:

PQ = 5y - 31

PT = 6x - 2y

QR = 2y + 5

PS = 4x + 4

SR = 7x - 17

Find the value of x:

PS = SR (congruent sides)

  • Substitute

[tex]4x + 4 = 7x - 17[/tex]

  • Collect like terms and solve for x

[tex]4x -7x = -4 - 17\\\\-3x = -21[/tex]

  • Divide both sides by -3

x = 7

Find the value of y:

PQ = RQ (since QT is the perpendicular bisector of PR, PT equals TR, therefore, triangles PQT and RQT are congruent).

  • Substitute

[tex]5y - 31 = 2y + 5[/tex]

  • Collect like terms and solve for y

[tex]5y - 2y = 31 + 5\\\\3y = 36\\\\\mathbf{y = 12}[/tex]

Find the length of each side by plugging in the value of x and y:

PQ = 5y - 31 = 5(12) - 31 = 29

PT = TR = 6x - 2y = 6(7) - 2(12) = 18

QR = 2y + 5 = 2(12) + 5 = 29

PS = 4x + 4 = 4(7) + 4 = 32

SR = 7x - 17 = 7(7) - 17 = 32

Find QT using Pythagorean Theorem:

[tex]QT = \sqrt{QR^2 - TR^2} \\\\QT = \sqrt{29^2 - 18^2} \\\\QT = 22.7[/tex]

Therefore, applying the Pythagorean Theorem and the definition of perpendicular bisector, the values of x and y, as well as the measures of each segment in the image are:

  • x = 7
  • y = 12
  • QT = 22.7
  • PQ = 29
  • PT = TR = 18
  • QR= 29
  • PS = 32
  • SR = 32

Learn more here:

https://brainly.com/question/1761937

Otras preguntas