Question

The length of a rectangular garden is 4m greater than the width. The area of the garden is 20m squared. Find the dimensions of the garden.

Answer 1

$L = length\\W = width\\L = W + 4\\A = 20 m^2\\A=L*W\\(W+4)(W)=20\\W^2+4W=20\\W^2+4W-20=0\\W=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\W=\frac{-4\pm\sqrt{16-(-80)}}{2}\\ W=\frac{-4\pm4\sqrt{6}}{2}\\W_1=2.9\hspace{3pt}and\hspace{3pt}W_2=-6.9\\ The\hspace{3pt}width\hspace{3pt}cannot\hspace{3pt}be\hspace{3pt}negative, \hspace{3pt}so\hspace{3pt}the\hspace{3pt}width\hspace{3pt}is\hspace{3pt}2.9m\\ length, L=2.90 + 4=6.9m\\ Answer:length=6.9m;width=2.9m$