Independent: Practice
Use the coordinates to find the length of each side of the rectangle.
Then find the perimeter. (Examples 1 and 2 )

Ask by Turner Allan. in the United States

Mar 11,2025

Question

Independent: Practice
Use the coordinates to find the length of each side of the rectangle.
Then find the perimeter. (Examples 1 and 2 )

Ask by Turner Allan. in the United States

Mar 11,2025

UpStudy AI · Accepted Answer

To find the length of each side of the rectangle and then calculate the perimeter, we will follow these steps:

1. **Identify the coordinates of the vertices of the rectangles.**
2. **Calculate the lengths of the sides using the distance formula.**
3. **Calculate the perimeter using the lengths of the sides.**

### Step 1: Identify the Coordinates

For the first rectangle:
- $$ D(1,2) $$
- $$ E(1,7) $$
- $$ F(4,7) $$
- $$ G(4,2) $$

For the second rectangle:
- $$ Q(0,0) $$
- $$ R(4,0) $$

### Step 2: Calculate the Lengths of the Sides

**For Rectangle DEFG:**
- Length $$ DE $$ (vertical side) = $$ |y_E - y_D| = |7 - 2| = 5 $$
- Length $$ DF $$ (horizontal side) = $$ |x_F - x_D| = |4 - 1| = 3 $$

**For Rectangle QR:**
- Length $$ QR $$ (horizontal side) = $$ |x_R - x_Q| = |4 - 0| = 4 $$
- Since it's a rectangle, the vertical side will be the same as the horizontal side, which we will assume to be $$ 0 $$ for this case.

### Step 3: Calculate the Perimeter

The perimeter $$ P $$ of a rectangle is given by the formula:
$$
P = 2 \times (\text{Length} + \text{Width})
$$

**For Rectangle DEF:**
- Length = 5
- Width = 3
$$
P_{DEFG} = 2 \times (5 + 3) = 2 \times 8 = 16
$$

**For Rectangle QR:**
- Length = 4
- Width = 0 (assuming it is a line segment)
$$
P_{QR} = 2 \times (4 + 0) = 2 \times 4 = 8
$$

### Final Results

- The perimeter of rectangle DEF is $$ 16 $$.
- The perimeter of rectangle QR is $$ 8 $$.

Thus, the lengths of the sides and the perimeters are calculated as follows:
- Rectangle DEF: Lengths = 5 and 3, Perimeter = 16
- Rectangle QR: Lengths = 4 and 0, Perimeter = 8
The lengths of the sides and perimeters are: - Rectangle DEF: Lengths = 5 and 3, Perimeter = 16 - Rectangle QR: Lengths = 4 and 0, Perimeter = 8

Independent: Practice
Use the coordinates to find the length of each side of the rectangle.
Then find the perimeter. (Examples 1 and 2 )

Upstudy AI Solution

Answer

Solution

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Independent: Practice Use the coordinates to find the length of each side of the rectangle. Then find the perimeter. (Examples 1 and 2 )

Upstudy AI Solution

Answer

Solution

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Independent: Practice
Use the coordinates to find the length of each side of the rectangle.
Then find the perimeter. (Examples 1 and 2 )