Final answer:
To find the dimensions of Jose's rectangular picture frame with an area of 120 cm² and a length that is 6 cm longer than the width, we set up a quadratic equation and solve for the width, which gives us 10 cm. The length thus is 16 cm, resulting in the frame being 10 cm by 16 cm.
Step-by-step explanation:
Jose is making a picture frame with a rectangular shape that has an area of 120 cm2. The frame's length is 6 cm longer than its width. To find the dimensions of the frame, let's set the width as x cm. Therefore, the length will be x + 6 cm. Using the area of a rectangle, which is length times width, we set up the equation x(x + 6) = 120.
Distributing the x gives x2 + 6x = 120. We then move all terms to one side to set the quadratic equation to zero: x2 + 6x - 120 = 0. This equation can be factored into (x + 12)(x - 10) = 0, giving us two possible solutions for x: -12 and 10. Since a negative width doesn't make sense for a physical object, we discard -12, leaving us with a width of 10 cm and a length of 16 cm.
Hence, the dimensions of Jose's picture frame are 10 cm by 16 cm.