Question

Quadrilateral RPQS is a rectangle. Label the missing measures.

Answer 1

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`

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`