Question

Wally Beige has painted a rectangular mural that is 10 ft tall and 12 ft wide. He plans to paint a border of equal width all the way around the outside of the mural. To end up with a border that has an area of 320 square ft, find the width of the border.

Answer 1

To find the width of the border for Wally Beige's mural, you need to set up an equation based on the dimensions of the mural and the desired area of the border. The equation involves the dimensions of the mural with the added border on each side and solves for the width of the border by subtracting the area of the mural from the area of the larger rectangle that includes the border.

Step-by-step explanation:

The question entails solving for the width of the border that Wally Beige plans to paint around his rectangular mural. To determine the width of this border, we have to consider the dimensions of the mural and the area the border is supposed to occupy. In this case, the mural has a height of 10 ft and a width of 12 ft.

Let x be the width of the border. The overall dimensions of the mural with the border included would be (10 + 2x) feet in height and (12 + 2x) feet in width since the border is added to both sides. The area of just the border is the area of the outer rectangle minus the area of the mural, which the student wants to equal 320 square feet. The area of the mural is 10 ft * 12 ft = 120 square feet. So the equation we need to solve is:

(10 + 2x)(12 + 2x) - 120 = 320

To find the value of x, expand the left side of the equation and then simplify to solve for x.