Answer:
QR = 5 units
RS = 10 units
Perimeter of QRST = 30 units
Step-by-step explanation:
The perimeter of a rectangle is given by the formula:
where
is the perimeter of the rectangle
is the length of the rectangle
is the width of the rectangle
Now, to find the width, QR, and the length, RS, of the rectangle, we are using the distance formula:
where
is the distance
are the coordinates of the first point
are the coordinates of the second point
- For QR:
The first point of QR is Q(-3, 0) and the second is R(0, 4), so ,
,
, and
.
Replacing values
- For RS
The first point of RS is R(0, 4) and the second is S(8, -2), so ,
,
, and
.
Replacing values
Now that we know that the width QR is 5 units and the length RS is 10 units, we can find the perimeter of our rectangle:
We can conclude that QR = 5 units, RS = 10 units, and the perimeter of rectangle QRST is 30 units.