Final answer:
To create an artwork with an area 60% greater than the original 10 inches by 13 inches Monet's drawing, the new dimensions when both width and height are increased by the same amount would be approximately 12.45 inches by 15.45 inches.
Step-by-step explanation:
The question involves a scenario where Jennifer wants to create an art piece inspired by Claude Monet's drawing Maisons prés de la mer, which is approximately 10 inches by 13 inches, with an area that is 60% greater than the original. To find the dimensions of Jennifer's artwork, we need to calculate the increased area and then determine the new width and height, assuming both dimensions are increased by the same proportion.
First, we calculate the original area of the drawing: 10 inches × 13 inches = 130 square inches. A 60% increase in area means the new area will be 130 square inches + (0.60 × 130 square inches) = 130 square inches + 78 square inches = 208 square inches.
To maintain the same aspect ratio, we let x be the amount we add to both the width and the height. So, the new dimensions will be (10 + x) inches by (13 + x) inches. To find x, we solve the following equation for the area: (10 + x)(13 + x) = 208.
Expanding the equation, we get: 130 + 10x + 13x + x^2 = 208. Simplifying, we have x^2 + 23x + 130 = 208. Subtracting 208 from both sides gives us x^2 + 23x - 78 = 0. Through factoring or using the quadratic formula, we find that x is approximately 2.45 inches.
Therefore, the new dimensions of Jennifer's artwork will be approximately (10 + 2.45) inches by (13 + 2.45) inches, which is 12.45 inches by 15.45 inches.