Question

Find the perimeter of rectangle EFGH , with vertices E(6,9) and F(4,9) , G(4,−5) , and H(6,−5) .(1 point)

Answer 1

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

The vertices of rectangle EFGH are:
- E(6, 9)
- F(4, 9)
- G(4, -5)
- H(6, -5)

1. **Calculate the length of side EF:**
Since E and F have the same y-coordinate, the distance between them can be found using the x-coordinates:
\[
EF = |x_E - x_F| = |6 - 4| = 2
\]

2. **Calculate the length of side EH:**
Since E and H have the same x-coordinate, the distance between them can be found using the y-coordinates:
\[
EH = |y_E - y_H| = |9 - (-5)| = |9 + 5| = |14| = 14
\]

3. **Find the perimeter of rectangle EFGH:**
The perimeter \( P \) of a rectangle can be calculated using the formula:
\[
P = 2(\text{length} + \text{width}) = 2(EF + EH)
\]
Substituting the side lengths we found:
\[
P = 2(2 + 14) = 2 \times 16 = 32
\]

Thus, the perimeter of rectangle EFGH is \( \boxed{32} \).