Final answer:
To calculate the width of the frame, represent it as 'w' and solve the quadratic equation (4/9 + 2w)^2 = 130 to find 'w'.
Step-by-step explanation:
To find the width of the frame around a photo that is 4/9 inches, with the total area of the framed photo being 130 square inches, you need to use the concept of quadratic equations because adding a frame of uniform width around a picture will increase both the length and the width by twice the frame's width.
Let's denote the frame width as 'w' inches. Therefore, the dimensions of the framed photo would be (4/9 + 2w) inches by (4/9 + 2w) inches. The area of the framed photo is the square of this sum, which equals 130 square inches.
(4/9 + 2w)^2 = 130
Solving the quadratic equation will give us the value of 'w', the width of the frame.