Question

the length of a rectangle is 6 centimeters less than its width. what are the dimensions of the rectangle if its area is 247 square centimeters?
the length of the rectangle is \boxed{} cm.
the width of the rectangle is \boxed{} cm.

Explanation:

Step1: Define variables for dimensions

Let width = $w$ cm. Then length = $w-6$ cm.

Step2: Set up area equation

Area of rectangle: $w(w-6)=247$
Expand: $w^2 -6w -247=0$

Step3: Solve quadratic equation

Factor the quadratic:
Find two numbers that multiply to $-247$ and add to $-6$: $-19$ and $13$.
So $(w-19)(w+13)=0$
Solutions: $w=19$ or $w=-13$ (discard negative width)

Step4: Calculate length

Length = $19-6=13$ cm

Answer:

The length of the rectangle is 13 cm.
The width of the rectangle is 19 cm.