A rectangle's width is 2 meters shorter than its length, [tex]$I$[/tex]. Its area is 168 square meters. Which equation can be used to find the length of the rectangle?
[tex]$I(I-2)=168$[/tex]
[tex]$I(I+2)=168$[/tex]
[tex]$2 l^2=168$[/tex]
[tex]$\frac{1}{2} l^2=168$[/tex]
Answer (1)
Let l be the length of the rectangle.
The width of the rectangle is l − 2 .
The area of the rectangle is given by the product of its length and width, so l ( l − 2 ) = 168 .
The equation that can be used to find the length of the rectangle is l ( l − 2 ) = 168 .
Explanation
Problem Analysis Let's analyze the problem. We are given that the width of a rectangle is 2 meters shorter than its length, which we'll call l . The area of the rectangle is 168 square meters. We need to find the equation that relates the length and width to the area.
Setting up the Equation Let l be the length of the rectangle. Since the width is 2 meters shorter than the length, the width is l − 2 . The area of a rectangle is given by the product of its length and width. Therefore, the area is l ( l − 2 ) . We are given that the area is 168 square meters, so we have the equation l ( l − 2 ) = 168 .
Finding the Equation The equation that can be used to find the length of the rectangle is l ( l − 2 ) = 168 .
Final Answer Therefore, the correct equation is l ( l − 2 ) = 168 .
Examples
Imagine you are designing a rectangular garden where the length is 2 meters more than the width. If you want the garden to cover an area of 168 square meters, you can use the equation l ( l − 2 ) = 168 to determine the length l of the garden. This type of problem is useful in various real-world scenarios, such as designing rooms, gardens, or any rectangular space where you need to determine the dimensions based on a given area and a relationship between the length and width.
