Question 997948
The area of a table top is 52 square feet, and twice the length is 3 feet shorter than two times the width. Find the perimeter of the table top.


let length be l
width be w

2l=2w-3

{{{l = (2w-3)/2 }}}


l * w = 52

substitute l 

{{{((2w-3)/2) * w =52}}}


multiply equation by 2

(2w-3 )*w = 52*2

{{{2w^2-3w =104}}}

{{{2w^2-3w-104=0}}}


{{{2w^2-16w+13w-104=0}}}

2w(w-8)+13(w-8)=0

(2w+13)(w-8)=0

If 2w+13 =0

then w = -7.5
not applicable

if w-8=0

the dimensions are 8 and 6.5 feet

w= 8