let

l = the length, l>0

w = the width, w>0

the length of the top of a table is 7 m greater than the width

l = 7 + w

the area is A = 78 m^2 and since the formula for the area is A = l*w we have

l*w = 78

plug l = 7 + w into the last equation

(7 + w)*w = 78

by solving we find

w = 6 m

click here to see the step by step solution of the equation

Click to see all the steps

l = 7 + 6

l = 13 m

the dimensions of the table are 13 meters x 7 meters.