An artist intends to paint a 60-square-foot mural on a large wall that is 18 ft wide and 11 ft tall. find the dimensions of the mural if the artist leaves a border of uniform width around it.
what formula do I use please?
taking off the width of w from each of the four sides, we have
(18-2w)(11-2w) = 60
now just wind w
or, look for two factors of 60 which differ by 7
5*12 = 60
...
To find the dimensions of the mural, considering that the artist leaves a border of uniform width around it, you can use the formula for the area of a rectangle.
1. Start by finding the area of the entire wall:
Area of the wall = width × height = 18 ft × 11 ft = 198 square feet.
2. Subtract the desired area of the mural from the area of the wall to find the area of the border:
Area of the border = Area of the wall - Area of the mural.
The desired area of the mural is 60 square feet, so the area of the border would be:
Area of the border = 198 square feet - 60 square feet = 138 square feet.
3. Since the border is of uniform width, you need to divide the area of the border by the width of the border to find the length of the border:
Area of the border = length of the border × width of the border.
Let's assume the width of the border is represented by 'x'. Therefore, we can write the equation:
138 square feet = length of the border × x.
4. Now, you need to choose a value for the width of the border. Once you have that, you can solve the equation to find the length of the border. Let's assume the width of the border is 3 feet.
Substituting the values into the equation:
138 square feet = length of the border × 3 feet.
Divide both sides of the equation by 3 to isolate the length of the border:
Length of the border = 138 square feet / 3 feet = 46 feet.
5. Now that you know the length of the border, you can find the dimensions of the mural by subtracting twice the width of the border from the original wall dimensions:
Length of the mural = Length of the wall - 2 × Width of the border
Width of the mural = Width of the wall - 2 × Width of the border
Substituting the known values:
Length of the mural = 11 ft - 2 × 3 ft = 11 ft - 6 ft = 5 ft
Width of the mural = 18 ft - 2 × 3 ft = 18 ft - 6 ft = 12 ft.
Therefore, the dimensions of the mural with a uniform border width of 3 feet would be 5 ft by 12 ft.