Questions: A rectangle has a length 2 m less than twice its width. When 2 m are added to the width, the resulting figure is a square with an area of 36 m^2. Find the dimensions of the original rectangle. The length of the original rectangle is and its width is

A rectangle has a length 2 m less than twice its width. When 2 m are added to the width, the resulting figure is a square with an area of 36 m^2. Find the dimensions of the original rectangle.

The length of the original rectangle is and its width is

Transcript text: A rectangle has a length 2 m less than twice its width. When 2 m are added to the width, the resulting figure is a square with an area of $36 \mathrm{~m}^{2}$. Find the dimensions of the original rectangle. The length of the original rectangle is $\square$ $\square$ and its width is $\square$ $\square$

Solution

Solution Steps

To find the dimensions of the original rectangle, we need to set up equations based on the given conditions. Let the width of the rectangle be $ w $. Then, the length of the rectangle is $ 2w - 2 $. When 2 m are added to the width, the width becomes $ w + 2 $, and the resulting square has an area of 36 m². Therefore, the side of the square is 6 m. We can set up the equation $ w + 2 = 6 $ to find $ w $, and then use it to find the length.

Step 1: Define Variables

Let the width of the rectangle be $ w $. According to the problem, the length $ l $ of the rectangle can be expressed as: \[ l = 2w - 2 \]

Step 2: Set Up the Equation for the Square

When 2 m are added to the width, the new width becomes: \[ w + 2 \] This new figure is a square with an area of $ 36 \, \text{m}^2 $. The side length of the square is given by: \[ s = \sqrt{36} = 6 \, \text{m} \] Thus, we have the equation: \[ w + 2 = 6 \]

Step 3: Solve for Width

Solving the equation $ w + 2 = 6 $: \[ w = 6 - 2 = 4 \, \text{m} \]

Step 4: Calculate Length

Now, substituting $ w $ back into the equation for length: \[ l = 2(4) - 2 = 8 - 2 = 6 \, \text{m} \]