The length of a rectangle is the width minus 8 units. The area of the rectangle is 9 units. What is the length, in units, of the rectangle?

Length of rectangle is 1 unit  Solution: Given that  Length of a rectangle is width minus 8 units. Area of rectangle = 9 square units Need to calculate the length of rectangle. Let us assume width of rectangle = x As Length is width minus 8,  Length of the rectangle = x – 8 [tex]\text{ Area of rectangle }=\text{ width of rectangle }\times \text{ Length of the rectangle }[/tex][tex]\text{ Area of rectangle }= x\times (x-8)[/tex][tex]\text { Area of rectangle }=\left(x^{2}-8 x\right)[/tex]As given that area of rectangle = 9 square units [tex]\begin{array}{l}{\Rightarrow x^{2}-8 x=9} \\\\ {\Rightarrow x^{2}-8 x-9=0}\end{array}[/tex]On solving above quadratic equation for x, we get [tex]\begin{array}{l}{\Rightarrow x^{2}-9 x+x-9=0} \\\\ {\Rightarrow x(x-9)+1(x-9)=0} \\\\ {\Rightarrow (x-9)(x+1)=0}\end{array}[/tex]When [tex]x-9 =9, x = 9[/tex]When [tex]x + 1 = 0, x = -1[/tex] As width cannot be negative, so considering x = 9  [tex]\text{ Length of rectangle }= x-8 = 9-8 = 1 \text{ unit }[/tex]Hence, Length of rectangle is 1 unit.