Given:
PQRS is a rectangle.
X is the midpoint of SR.
To find:
The measure of QX.
Solution:
It is given that X is the midpoint of SR. Draw a perpendicular on PQ from point X as shown in the below figure.
Now, the line XY divides the rectangle PQRS into two equal squares of sides 4 units.
The diagonal of a square is:
[tex]d=a\sqrt{2}[/tex]
Where, a is the side length of the square.
QX is the diagonal of the square whose side length is 4 units. So, the length of QX is:
[tex]d=4\sqrt{2}[/tex]
[tex]d=5.656854[/tex]
[tex]d\approx 5.7[/tex]
Therefore, the measure of segment QX is about 5.7 units.
