Finding the perimeter or area of a rectange gength of a rectangle is four times its width.
The le area of the rectangle is , find its perimeter.

Question

Finding the perimeter or area of a rectange gength of a rectangle is four times its width. The le area of the rectangle is $$ 400 \mathrm{~m}^{2} $$, find its perimeter.

UpStudy AI · Accepted Answer

To find the perimeter of the rectangle, let's break down the problem step by step.

### Given:
1. **Length (ℓ)** of the rectangle is four times its **width (w)**:
   $$
   \ell = 4w
   $$
2. **Area (A)** of the rectangle is 400 square meters:
   $$
   A = \ell \times w = 400 \, \text{m}^2
   $$

### Steps to Find the Perimeter:

1. **Express the Area in Terms of Width:**
   Substitute the expression for length into the area equation:
   $$
   \ell \times w = 400 \Rightarrow 4w \times w = 400 \Rightarrow 4w^2 = 400
   $$
   
2. **Solve for Width (w):**
   $$
   w^2 = \frac{400}{4} = 100 \Rightarrow w = \sqrt{100} = 10 \, \text{m}
   $$
   
3. **Find the Length (ℓ):**
   $$
   \ell = 4w = 4 \times 10 = 40 \, \text{m}
   $$
   
4. **Calculate the Perimeter (P):**
   The perimeter of a rectangle is given by:
   $$
   P = 2(\ell + w) = 2(40 + 10) = 2 \times 50 = 100 \, \text{m}
   $$

### **Answer:**
The perimeter of the rectangle is **100 meters**.
The perimeter of the rectangle is 100 meters.

Finding the perimeter or area of a rectange gength of a rectangle is four times its width.
The le area of the rectangle is , find its perimeter.

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Finding the perimeter or area of a rectange gength of a rectangle is four times its width. The le area of the rectangle is , find its perimeter.

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Finding the perimeter or area of a rectange gength of a rectangle is four times its width.
The le area of the rectangle is , find its perimeter.