Given:
PQRS is a rectangle.
[tex]PS=5\ cm,\ PR=13\ cm[/tex]
To find:
The length of SR and QS.
Solution:
We know that, all interior angles of a rectangle are right angle. So, [tex]\angle S=90^\circ[/tex].
According to the Pythagoras theorem, in a right angle triangle,
[tex]Hypotenuse^2=Base^2+Perpendicular^2[/tex]
Using Pythagoras theorem in triangle PRS, we get
[tex]PR^2=PS^2+SR^2[/tex]
[tex]13^2=5^2+SR^2[/tex]
[tex]169-25=SR^2[/tex]
[tex]144=SR^2[/tex]
Taking square root on both sides.
[tex]\sqrt{144}=SR[/tex]
[tex]12=SR[/tex]
So, the measure of SR is 12 cm.
We know that the diagonals of a rectangle are equal. PR and QS are the diagonals of the rectangle PQRS. So,
[tex]PR=QS[/tex]
[tex]13=QS[/tex]
Therefore, the length of SR is 12 cm and the length of QS is 13 cm.
