Final answer:
To find the dimensions of a rectangular table with an area of 11.9 square feet and a width that is 2.6 feet less than its length, we set up and solve a quadratic equation representing the area. Calculating the positive value of length using this equation, we can then find the width by subtracting 2.6 feet from the length.
Step-by-step explanation:
The question asks to find the dimensions of a rectangular table when the width is 2.6 feet less than its length and the area is 11.9 square feet. To find the dimensions, we can let the length be represented by x feet. Thus the width will be x - 2.6 feet. The area of a rectangle is found by multiplying the length by the width, so we create the equation x(x - 2.6) = 11.9. Through solving this quadratic equation, we can find the value of x which represents the length of the table, then use it to calculate the width.
To solve the quadratic equation, we can set it to zero by subtracting 11.9 from both sides: x^2 - 2.6x - 11.9 = 0. We can now use the quadratic formula to find the values of x: x = [-(-2.6) ± √((-2.6)^2 - 4(1)(-11.9)) ] / 2(1). After calculating, we will get two possible solutions for x, but only one solution will be practical since length and width must be positive. The practical solution will give us the length of the table, and subtracting 2.6 from it will give us the width.