A photograph measuring 8 inches by 6 inches is surrounded by a mat. The mat has the same width on all sides of the photograph. The photograph and mat are put into a glass photo frame which just covers the outside of the mat.
If the area of the glass surface is 120 square inches, whats the width of the mat?
10 inches
To find the width of the mat, we first need to determine the dimensions of the photograph with the mat.
Given that the photograph measures 8 inches by 6 inches, we can represent its dimensions as length = 8 inches and width = 6 inches.
Let's assume the width of the mat to be x inches.
To find the dimensions of the photograph with the mat, we need to add twice the width of the mat to the length and width of the photograph.
The length of the photograph with the mat will be 8 + 2x inches, and the width will be 6 + 2x inches.
Next, we need to find the area of the photograph with the mat.
The area is calculated by multiplying the length by the width.
So, (8 + 2x) * (6 + 2x) = Area of photograph with mat.
The glass photo frame covers the outside of the mat, which means it covers the entire area of the photograph with the mat.
Given that the area of the glass surface is 120 square inches, we set up the equation:
(8 + 2x) * (6 + 2x) = 120
Now, we can solve this equation to find the value of x - the width of the mat.