Answer:
\(w=x-9\)
Step-by-step explanation:
It is given that area of the rectangle is \(\left (x^{2} -x-72\right )\:m^{2}\) and length of the rectangle is \((x+8) \:m\)
We know that area of rectangle is length\(\times\)width
We have, \(l\times b=x^{2}-x-72\)
\(w=\frac{x^{2}-x-72}{x+8} \:\:\left [ \because l=x+8 \right ]\)
\(w=\frac{x^{2}-9x+8x-72}{x+8}\)
\(w=\frac{x\left ( x-9 \right )+8\left ( x-9 \right )}{x+8}\)
\(w=\frac{\left ( x+8 \right )\left ( x-9 \right )}{x+8}\)
\(w=x-9\)
Hence, width of the rectangle is \(w=(x-9)\,m\)
