Question 21574
Let the length of the table top be L and its width W.
L = 5W-8

The area of a rectangle is:
{{{A = L*W}}} Substitute L = 5W-8
{{{A = (5W-8)(W)}}}
{{{A = 5W^2-8W}}} But A = 48 sq.ft.
{{{48 = 5W^2-8W}}} Subtract 48 from both sides.
{{{5W^2-8W-48 = 0}}} Solve by factoring.
{{{(5W+12)(W-4) = 0}}} Apply the zero product principle.
{{{(5W+12) = 0}}} and/or {{{W-4) = 0}}}
If {{{5W+12 = 0}} then, 5W = -12}}} and {{{W = -12/5}}} Discard this solution as the width can only be positive.
If {{{W-4 = 0}}} then, {{{W = 4}}}

The width is 4 feet.
The length, L, is 5(4)-8 = 20 - 8 = 12 feet.

Check:

A = L*W
A = 12*4
A = 48 sq.ft.