Finding the perimeter or area of a rectangle given one of these values
The length of a rectangle is four times its width.
If the area of the rectangle is , find its perimeter.
Wyd

Question

Finding the perimeter or area of a rectangle given one of these values
The length of a rectangle is four times its width.
If the area of the rectangle is

, find its perimeter.
Wyd

UpStudy AI · Accepted Answer

To find the perimeter of the rectangle given the area and the relationship between its length and width, follow these steps:

1. **Define the Variables:**
   - Let $$ w $$ represent the width of the rectangle.
   - Given that the length $$ l $$ is four times the width, we can express the length as:
     $$
     l = 4w
     $$

2. **Use the Area to Find the Width:**
   - The area $$ A $$ of a rectangle is given by:
     $$
     A = l \times w
     $$
   - Given that the area is $$ 100 \, \text{yd}^2 $$:
     $$
     100 = 4w \times w
     $$
     $$
     100 = 4w^2
     $$
     $$
     w^2 = \frac{100}{4} = 25
     $$
     $$
     w = \sqrt{25} = 5 \, \text{yd}
     $$

3. **Find the Length:**
   - Using $$ l = 4w $$:
     $$
     l = 4 \times 5 = 20 \, \text{yd}
     $$

4. **Calculate the Perimeter:**
   - The perimeter $$ P $$ of a rectangle is given by:
     $$
     P = 2(l + w)
     $$
     $$
     P = 2(20 + 5) = 2 \times 25 = 50 \, \text{yd}
     $$

**Answer:**  
The perimeter of the rectangle is **50 yards**.
The perimeter of the rectangle is 50 yards.

Finding the perimeter or area of a rectangle given one of these values
The length of a rectangle is four times its width.
If the area of the rectangle is , find its perimeter.
Wyd

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Finding the perimeter or area of a rectangle given one of these values The length of a rectangle is four times its width. If the area of the rectangle is , find its perimeter. Wyd

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Latest Geometry Questions

Finding the perimeter or area of a rectangle given one of these values
The length of a rectangle is four times its width.
If the area of the rectangle is , find its perimeter.
Wyd