Question

Rectangle ABCD
has the coordinates A(0,0)
and B(3,3)
, and the diagonal distance from point B
to point D
is 8 units. Using the coordinates given and the diagonal distance, what is the approximate perimeter of the rectangle? Round each calculation to the tenths place.(1 point)
Responses

Answer 1

To find the perimeter of rectangle ABCD with given points A(0,0) and B(3,3) and the diagonal distance from B to D being 8 units, we can follow these steps:

1. **Identify Coordinates of Points**:
- A(0,0)
- B(3,3)
- To find the coordinates of D, we first need to figure out where point C is located.

2. **Calculate the Length of Sides**:
- The distance from A to B can be calculated using the distance formula:
\[
AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
\[
AB = \sqrt{(3 - 0)^2 + (3 - 0)^2} = \sqrt{9 + 9} = \sqrt{18} \approx 4.2
\]

- We know that the diagonal BD is 8 units.

3. **Using the Pythagorean Theorem**:
Since ABCD is a rectangle, we can use the Pythagorean theorem:
\[
BD^2 = AB^2 + AD^2
\]
Substituting the known values:
\[
8^2 = 4.2^2 + AD^2
\]
\[
64 = 17.64 + AD^2
\]
\[
AD^2 = 64 - 17.64 \approx 46.36
\]
\[
AD \approx \sqrt{46.36} \approx 6.8
\]

4. **Finding Other Sides**:
The width (AB) is approximately 4.2 units and the length (AD) is approximately 6.8 units.

5. **Calculating Perimeter**:
The perimeter of a rectangle is given by:
\[
P = 2 \times (length + width) = 2 \times (AD + AB)
\]
\[
P \approx 2 \times (6.8 + 4.2) = 2 \times 11 \approx 22
\]

Thus, rounding to the tenths place, the approximate perimeter of rectangle ABCD is **22.0 units**.