the width of a rectangle is 3cm less than twice the length.If the area of the rectangle is 47cm2^,find the length and width

Question

Quadratic equation should be used to solve problem

Answer 1

If the length is x then width=2x-3 and area=x(2x-3)=47.

So 2x^2-3x-47=0. This can be written: x^2-3x/2=47/2.

Completing the square we get: x^2-3x/2+9/16=47/2+9/16.

(x-3/4)^2=(376+9)/16; x-3/4=±√385/4=±4.90535 approx. So x=3/4±4.90535, but x must be positive so x=5.655 approx. That's the length, so width=2x-3=8.311 approx. Multiply them and we get 47 to a close approximation.