Answer:
4x² + 22x - 1 = 0
Step-by-step explanation:
The painting is in the form of a rectangle with measurement of 5 feet width and 6 feet length. Let us assume that the frame has a thickness of x feet, hence:
Length of painting and frame = 6 + 2x, breadth of painting and frame = 5 + 2x
Therefore:
Area of painting and frame = length of painting and frame * breadth of painting and frame
Given that the area of painting and frame is 31 ft², substituting gives:
31 = (6 + 2x)(5 + 2x)
31 = 30 + 12x + 10x + 4x²
31 = 30 + 22x + 4x²
4x² + 22x + 30 = 31
4x² + 22x - 1 = 0
