Final answer:
To find the length of the rectangular picture with an area of 96in² and width being 4 in less than the length, we use the area formula of a rectangle. We set up and solve a quadratic equation which gives us the width as 8 inches and the length as 12 inches. Since the width can't be negative, the width must be 8 inches. Hence, the length is w + 4 = 8 + 4 = 12 inches.
Step-by-step explanation:
The question asks us to find the length of a rectangular picture given the area is 96in² and the width is 4 in less than the length. The width can be expressed as w, and the length as w + 4 since the width is 4 inches shorter than the length. The area of a rectangle is found by multiplying length and width, so we set up our equation as w(w + 4) = 96.
To find the values of w, we solve the quadratic equation:
- w² + 4w - 96 = 0
- Factorize: (w + 12)(w - 8) = 0
- Solve for w: w = -12 or w = 8
Since the width can't be negative, the width must be 8 inches. Hence, the length is w + 4 = 8 + 4 = 12 inches.