Question

A landscaper has enough cement to make a patio with an area of 150 Sq ft. The homeowner wants the length of the patio to be 6 ft longer than the width. What dimensions should be used for the patio? Round your answer to the nearest tenth of a foot.

Answer 1

`A=lw=150\\l=w+6\\(w+6)w=150\\w^2+6w=150\\w^2+6w-150=0\\w=(-b+-√(b^2-4ac))/(2a)\\w=(-(6)+-√((6)^2-4(1)(-150)))/(2(1))\\w=(-6+-√(36+600))/(2)\\w=(-6+-√(636))/(2)\\w=(-6+-2√(159))/(2)\\w=-3+-√(159)>0\\w=-3+√(159)\\\\l=(-3+√(159))+6\\l=3+√(159)`

Width = -3 + sqrt(159)
Length = 3 + sqrt(159)