Question

area of rectangle is 66. length is 4 more than 6 times width .find length and width.

Answer 1

Let the width = x units
length = (6x + 4) units
area = 66 sq. units
$$\begin{gathered} \Rightarrow \mathrm{length}\times \mathrm{breadth}=66 \\ \Rightarrow x(6x+4)=66 \\ \Rightarrow 6x^2+4x-66=0 \\ \Rightarrow 3x^2+2x-33=0 \\ \Rightarrow 3x^2-9x+11x-33=0 \\ \Rightarrow 3x(x-3)+11(x-3)=0 \\ \Rightarrow (3x+11)(x-3)=0 \\ \Rightarrow 3x+11=0orx-3=0 \\ \Rightarrow x=-\frac{11}{3}\left(\mathrm{rejected}\right)orx=3 \end{gathered}$$

so, width = 3 units
length = 22 units