Video Transcript
The length of a rectangle is nine more than its width; the area of the rectangle is no more than 20. Write an inequality for the area of the rectangle, 𝐴, in terms of the width, 𝑊.
Let’s begin by drawing the rectangle. We are told that the width of the rectangle is 𝑊. The length is nine more than this. So this is equal to 𝑊 plus nine. As the area is no more than 20, we know we will have an inequality instead of an equation.
In order to calculate the area of any rectangle, we multiply the length by the width. In this case, our area, 𝐴, is equal to 𝑊 plus nine multiplied by 𝑊. As multiplication is commutative, this can be rewritten as 𝑊 multiplied by 𝑊 plus nine. As the area is no more than 20, this expression must be less than or equal to 20.
The inequality for the area of the rectangle, 𝐴, in terms of the width, 𝑊, is 𝑊 multiplied by 𝑊 plus nine is less than or equal to 20. Whilst we don’t need to in this question, we could then solve this inequality to calculate the maximum value of the width, 𝑊.
