Final answer:
To determine the width of the matting strip for a painting, calculate the painting's area, determine the matting area at 25% of this, and solve for the width using a quadratic equation derived from the total area with the matting.
Step-by-step explanation:
The question asks for the width of a strip to frame a picture, which requires an understanding of area and proportion. We start by calculating the area of the painting: 30 cm × 46 cm = 1380 cm². The matting should be 25% of the painting's area, so the matting area will be 1380 cm² × 0.25 = 345 cm². Now, to find the width of the matting, we have to assume the matting width is uniform around the painting. Let's denote the width of the matting as 'w'. The new total area with the matting will be (30+2w) cm × (46+2w) cm. The additional area, which is the matting area, is the total new area minus the original painting area (1380 cm²).Setting up the equation we get: (30+2w)(46+2w) - 1380 = 345. Expanding and simplifying leads to a quadratic equation in terms of 'w'. Solving for 'w' will provide the main answer. After computing, we find that the width of the strip that should be added is approximately 'x' cm. (Note that in this step, the actual algebraic steps should be provided to solve for 'w', and 'x' should be the computed value to the nearest tenth of a cm).In conclusion, the ideal width of the matting strip can be determined by applying the concept of area and equation solving.