Answer:
Part 1) [tex]PR=9\ units[/tex]
Part 2) [tex]PQ=12\ units[/tex]
Part 3) [tex]PS=15\ units[/tex]
part 4) [tex]QR=15\ units[/tex]
Part 5) [tex]RT=7.5\ units[/tex]
Step-by-step explanation:
we know that
In a rectangle opposite sides are parallel and congruent
The measure of each interior angle is 90 degrees
The diagonals are congruent and bisect each other
step 1
Find the length of side PR
we know that
[tex]PR=QS[/tex] ----> by opposite sides
we have
[tex]QS=9\ units[/tex]
therefore
[tex]PR=9\ units[/tex]
step 2
Find the length of side PQ
we know that
[tex]PQ=RS[/tex] ----> by opposite sides
we have
[tex]RS=12\ units[/tex]
therefore
[tex]PQ=12\ units[/tex]
step 3
Find the length of diagonal PS
we know that
[tex]PS=2PT[/tex]---> the diagonals bisect each other
we have
[tex]PT=7.5\ units[/tex] ---> given problem
therefore
[tex]PS=2(7.5)=15\ units[/tex]
step 4
Find the length of diagonal QR
we know that
[tex]QR=PS[/tex]---> the diagonals are congruent
we have
[tex]PS=15\ units[/tex]
therefore
[tex]QR=15\ units[/tex]
step 5
Find the length of RT
we know that
[tex]QR=2RT[/tex]---> the diagonals bisect each other
we have
[tex]QR=15\ units[/tex]
substitute
[tex]15=2RT\\RT=7.5\ units[/tex]
