Respuesta :

According to the attachment at point it makes the angle of 90° with both triangles, so;
SR = SQ
2x + 8 = 8x - 4
and if we find the value of x, we will find the value of  line segment SR
8x -2x = 8+4
6x = 12
x = 12/6
x = 2
now put the value of x in SR = 2x + 8 = 2(2) + 8 = 4 + 8 = 12
SR = 12

The length of segment SR is [tex]12[/tex].

According to the question,

[tex]TQ=TR[/tex] (Given)

[tex]\angle T=90[/tex] degree

Let [tex]TS=x[/tex]

and, [tex]TR=y[/tex]

also, [tex]TQ=y[/tex]

Apply Pythagoras theorem in triangle [tex]RTS[/tex] as-

[tex]RS^{2} =TR^2+TS^2[/tex]

[tex](2x+8)^2=y^2+x^2[/tex]-----------eq [tex]1[/tex]

Apply Pythagoras theorem in triangle [tex]STQ[/tex] as-

[tex]QS^{2} =TQ^2+TS^2[/tex]

[tex](8x-4)^2=y^2+x^2[/tex]-----------eq [tex]2[/tex]

Equate equations [tex]1\; and \; 2[/tex],

[tex](2x+8)^2=(8x-4)^2[/tex]

Square the above equation,

[tex](2x+8)=(8x-4)\\8x-2x=8+4\\6x=12\\x=2[/tex]

The value of the length of the segment SR is-

[tex]SR=2x+8\\SR=2\times2 + 8\\SR=12[/tex]

The length of segment SR is [tex]12[/tex].

Learn more about Pythagoras theorem here:

https://brainly.com/question/10174253?referrer=searchResults

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