The small medium from in center to all the three sides of triangle is equal.
The length of the SQ is 5 units.
What is in-center of triangle?
The in-center of a triangle is the point of intersection of all the three interior angle bisectors of a triangle.
The small medium from in center to all the three sides of triangle is equal. Thus,
[tex]SQ=SP=SR[/tex]
Given information-
The length of MR is 12 units.
The length of MS is 13 units.
In the [tex]\Delta MRS, \angle MRS[/tex] is the right angle triangle. Thus by the Pythagoras theorem,
[tex]MS^2=MR^2+RS^2[/tex]
Rewrite the equation as,
[tex]RS^2=MS^2-MR^2[/tex]
Put the values,
[tex]RS^2=13^2-12^2\\RS^2=169+144\\RS^2=25\\RS=\sqrt{25}\\RS=5\\[/tex]
Thus the length of RS is 5 units. As the length of RS is equal tot he length of the SQ. Thus,
[tex]SQ=RS=5[/tex]
Hence the length of the SQ is 5 units.
Learn more about the in center of the triangle here;
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