Final answer:
To find the width of the rectangle with an area of 20 cm² and a height that is 4 cm longer than thrice the width, we set up and solve a quadratic equation resulting from the area formula.
Step-by-step explanation:
The area of a rectangle can be calculated by multiplying its width by its height. Given that the area of the rectangle is 20 cm2 and the height is described as being 4 cm longer than thrice the width, we can set up an equation to find the width. Let's denote the width as 'w' and the height as 'h = 3w + 4'. The area equation becomes:
Area = width × height
20 = w × (3w + 4)
Now, we need to solve this quadratic equation for 'w' to find the width of the rectangle. Expanding and rearranging,
20 = 3w2 + 4w
3w2 + 4w - 20 = 0
This equation can be solved by factoring or using the quadratic formula. After finding the value of 'w', we can conclude the width of the rectangle in centimeters.