The area of the blue border is the difference between the area of the entire wall and the white rectangle.
1.4 feet
Practice makes perfect
We want to paint a wall by painting a blue border with width x around a white rectangle.
We are asked to find the approximate width x that makes the area of the blue border and the area of the white rectangle the same. To do so, we will first find the mentioned areas one by one and then set them equal. Let's begin by finding the area of the white rectangle.
Area of the White Rectangle
We can find the side lengths of the white rectangle by using the given figure.
From here we can write an expression for the area of the white rectangle.
To find the area of the border we will subtract the area of the white rectangle from the area of the entire wall.
Area of the Blue Border = Area of the Wall - Area of the White Rectangle
We found the area of the white rectangle in the previous subheading. We will find the area of the entire wall as well.
Area of the Wall &= 8* 12
&= 96
Now we are ready to write an expression for the area of the blue border.
Since the width of the entire wall is 8 feet, the width of the border needs to be smaller than 8 feet.
x_1 ≈ 8.6 x_2 ≈ 1.4
Therefore, x is approximately 1.4 feet.
