A border of uniform width is placed around a rectangular photograph that measures 8 inches by 10 inches. If the area of the border is 144 square inches, what is the width of the border, in inches?

Explanation: Let \(x\) be the width of the border. Photograph dimensions: Length \(L = 10\) inches, Breadth \(B = 8\) inches. Area of photograph = \(10 \times 8 = 80\) sq inches. Dimensions of photograph with border: New Length \(L' = 10 + 2x\), New Breadth \(B' = 8 + 2x\). Area of photograph with border = \((10 + 2x)(8 + 2x)\). Area of border = Area of photograph with border - Area of photograph. Given Area of border = 144 sq inches. \((10 + 2x)(8 + 2x) - 80 = 144\). \(80 + 20x + 16x + 4x^2 - 80 = 144\). \(4x^2 + 36x = 144\). \(4x^2 + 36x - 144 = 0\). Divide by 4: \(x^2 + 9x - 36 = 0\). Factor the quadratic equation: \((x + 12)(x - 3) = 0\). Since the width \(x\) must be positive, \(x = 3\).