Final answer:
To find the dimensions of the rectangle, a quadratic equation was set up using the given area and the relationship between length and width. Solving it provided the width of 1.25 cm and the length of 3.75 cm, excluding the non-sensical negative width solution.
Step-by-step explanation:
The question asks to find the dimensions of a rectangle given that its length is 4 cm less than three times its width, and it has an area of 15 cm². To solve this, we set up an equation where the width of the rectangle is represented by w, and the length is then 3w - 4 cm. The area is width times length, so the equation is w × (3w - 4) = 15. By solving this quadratic equation, we would find the width and thereafter, the length by substituting the width back into the length expression.
Let's solve the equation:
w(3w - 4) = 15
3w^2 - 4w - 15 = 0
Factoring the quadratic equation, we get two potential solutions for the width. After factoring out the possible solutions, we find that the width of the rectangle is 1.25 cm and the length, using the expression 3w - 4, is 3.75 cm.
Note: In this scenario, we've ignored the negative solution as a negative width does not make sense in the context of measuring a physical rectangle.