Question

Quadrilateral RPQS is a rectangle. Label the missing measures.

Answer 1

Answer:

Part 1) $PR=9\ units$

Part 2) $PQ=12\ units$

Part 3) $PS=15\ units$

part 4) $QR=15\ units$

Part 5) $RT=7.5\ units$

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

$PR=QS$ ----> by opposite sides

we have

$QS=9\ units$

therefore

$PR=9\ units$

step 2

Find the length of side PQ

we know that

$PQ=RS$ ----> by opposite sides

we have

$RS=12\ units$

therefore

$PQ=12\ units$

step 3

Find the length of diagonal PS

we know that

$PS=2PT$---> the diagonals bisect each other

we have

$PT=7.5\ units$ ---> given problem

therefore

$PS=2(7.5)=15\ units$

step 4

Find the length of diagonal QR

we know that

$QR=PS$---> the diagonals are congruent

we have

$PS=15\ units$

therefore

$QR=15\ units$

step 5

Find the length of RT

we know that

$QR=2RT$---> the diagonals bisect each other

we have

$QR=15\ units$

substitute

$15=2RT\\RT=7.5\ units$