The equation A(w)=w2+5w represents the relationship between the area in square units
and the width of a rectangle whose length is 5 units longer than its width.
To find the relationship between the area and the width of a rectangle, we can analyze the equation A(w) = w^2 + 5w.
In this equation, A(w) represents the area of the rectangle in square units, and w represents the width of the rectangle. The length of the rectangle is 5 units longer than its width, which means the length can be represented by w + 5.
The formula for the area of a rectangle is length multiplied by width. Therefore, using the given information, we can set up the equation:
A(w) = (w + 5)w
Multiplying w by w + 5, we have:
A(w) = w^2 + 5w
So, the equation A(w) = w^2 + 5w represents the relationship between the area in square units and the width of a rectangle whose length is 5 units longer than its width.
To find the area of the rectangle, we can use the equation A(w) = w^2 + 5w, where A(w) represents the area in square units and w represents the width of the rectangle.
Step 1: Understand the equation
The equation A(w) = w^2 + 5w represents the relationship between the area and the width of the rectangle. The area is calculated by taking the width squared (w^2) and adding 5 times the width (5w).
Step 2: Substitute values
If we have a specific value for the width, we can substitute it into the equation to find the corresponding area. Let's say the width of the rectangle is 10 units.
Step 3: Calculate the area
Substituting w = 10 into the equation, we get:
A(10) = (10)^2 + 5(10)
= 100 + 50
= 150
So, when the width is 10 units, the area of the rectangle is 150 square units.