Question

The length of a rectangle is 4 units less than twice the width. What is the length if the area of the rectangle is 160 square units?Enter your answer as a number, like this: 42Do not enter any units.

Answer 1

Let x be the width of the rectangle, then (2x-4) = length.

$x(2x-4)=160 \\ 2x^2-4x-160=0 \ \ |:2 \\ x^2-2x-80=0 \\ D=b^2-4ac=(-2)^2-4*1*80=4+320=324 \\ x_{1,2}= \frac{-bб \sqrt{D} }{2a} \\ x_{1}= \frac{2- \sqrt{324} }{2}= \frac{2-18}{2}=-8 \ \ \ \O \\ x_{2}= \frac{2+ \sqrt{324} }{2}= \frac{2+18}{2}=10 \ units \ (width) \\ \\ length=2*10-4=16 \ units$

Answer: 16.