Question

Find the perimeter of rectangle ABCD , with vertices A(1,7) , B(4,7) , C(4,−4) , and D(1,−4) .(1 point)

Answer 1

To find the perimeter of rectangle ABCD, we first need to calculate the lengths of its sides.

Given the vertices:
- A(1, 7)
- B(4, 7)
- C(4, -4)
- D(1, -4)

1. **Calculate the length of side AB:**
Since A and B share the same y-coordinate, the length can be calculated by finding the difference in the x-coordinates:
\[
AB = |x_B - x_A| = |4 - 1| = 3
\]

2. **Calculate the length of side AD:**
Since A and D share the same x-coordinate, the length can be calculated by finding the difference in the y-coordinates:
\[
AD = |y_A - y_D| = |7 - (-4)| = |7 + 4| = 11
\]

3. **Calculate the perimeter:**
The perimeter \(P\) of a rectangle is given by the formula:
\[
P = 2 \times (length + width)
\]
In this case, the length \(AB = 3\) and the width \(AD = 11\):
\[
P = 2 \times (3 + 11) = 2 \times 14 = 28
\]

Thus, the perimeter of rectangle ABCD is \(\boxed{28}\).