The width of a rectangle is $$ 6 y-7.5 $$ feet and the length is $$ 7.5 y+8 $$ feet. Find the perimeter of the rectangle.

Question

UpStudy AI · Accepted Answer

To find the perimeter of the rectangle, we'll use the formula:

$$
\text{Perimeter} (P) = 2 \times (\text{Length} + \text{Width})
$$

Given:
- **Width** = $$ 6y - 7.5 $$ feet
- **Length** = $$ 7.5y + 8 $$ feet

**Step 1: Plug the values into the perimeter formula**

$$
P = 2 \times \left( (7.5y + 8) + (6y - 7.5) \right)
$$

**Step 2: Combine like terms inside the parentheses**

$$
P = 2 \times \left( 7.5y + 6y + 8 - 7.5 \right)
$$
$$
P = 2 \times \left( 13.5y + 0.5 \right)
$$

**Step 3: Distribute the 2**

$$
P = 2 \times 13.5y + 2 \times 0.5
$$
$$
P = 27y + 1
$$

**Final Answer:**

The perimeter of the rectangle is $$ 27y + 1 $$ feet.
The perimeter of the rectangle is $$ 27y + 1 $$ feet.

The width of a rectangle is \( 6 y-7.5 \) feet and the length is \( 7.5 y+8 \) feet. Find the perimeter of the rectangle.