Question 850210
the area ; A =WL
w=width
L=length
........
now
" rectangle is 5 centimeters longer than its width."means;
length=5+W
..........
The area is 24 ,MEANS;
W*L=24
........
now we have 2 equations 
the first one is length=5+W
and the second one is W*L=24
sub the value of length in second equation
w*L=24
W*(5+w)=24
w*5+W*W=24
5w+w^2=24
by simple algebra find value of w
w^2+5w-24=0
(w+8)(w-3)=0
so 
w=3 or w=-8
we cross out w=-8 (because we can not have a negative value for length)
so we only use w=3 cm
...................
now 
sub value of w in the firs equation 
which is 
length =5+w
length=5+(3)
length=8 cm
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good luck :)