The length of a side of the square picture, obtained using the quadratic formula is about 8.9 centimeters
The steps used to find the length of the square picture is as follows;
The complete question obtained from a similar question found through search can be presented as follows;
A squire picture is mounted in a frame 1 cm wide. The area of the picture is 2/3 of the total area. Find the length of the side of the picture
Let s represent the side length of the square, we get;
Area of the square picture = s²
Total length of the picture and the frame = s + 2
Total area of the picture and the frame = (s + 2)²
Therefore; (2/3) × (s + 2)² = s²
(2·s² + 8·s + 8)/3 = s²
2·s² + 8·s + 8 = 3·s²
3·s² - 2·s² - 8·s - 8 = 0
s² - 8·s - 8 = 0
s = (8 ± √((-8)² - 4 × 1 × (-8)))/(2 × 1)
s ≈ 8.9, and s ≈ -0.9
Making use of only the positive side lengths, we get;
s ≈ 8.9 cm
The length of a side of the picture is about 8.9 cm