Question

What is the perimeter of rectangle STUV?
V =(-7,5)
U =(-6,5)
S =(-7,0)
T =(-6,0)
Perimeter = ______ Units

Answer 1

To find the perimeter of rectangle STUV, we first need to determine the lengths of its sides.

1. **Identify the vertices of the rectangle:**
- V = (-7, 5)
- U = (-6, 5)
- S = (-7, 0)
- T = (-6, 0)

2. **Calculate the lengths of the sides:**
- **Length of side SU (or VT)**: The distance between points S and U, or V and T, is the difference in the x-coordinates since they share the same y-coordinate.
\[
\text{Length SU} = |x_U - x_S| = |-6 - (-7)| = |-6 + 7| = |1| = 1 \text{ unit}
\]

- **Length of side ST (or UV)**: The distance between points S and T, or U and V, is the difference in the y-coordinates since they share the same x-coordinate.
\[
\text{Length ST} = |y_S - y_T| = |0 - 5| = |-5| = 5 \text{ units}
\]

3. **Calculate the perimeter of the rectangle:**
The formula for the perimeter \( P \) of a rectangle is given by:
\[
P = 2 \times ( \text{length} + \text{width} )
\]
Substituting the calculated lengths:
\[
P = 2 \times (1 + 5) = 2 \times 6 = 12 \text{ units}
\]

Thus, the perimeter of rectangle STUV is **12 units**.