The length of a photograph is 3cm less than twice the width. the area is 54cm^2. find the dimensions of the photograph.

W= width
l= length= 2w-3

Area= length * width
A= lw
substitute l=2w-3 for l
54= (2w-3)(w)
54= 2w^2 - 3w
subtract 54 from both sides
0= 2w^2 - 3w - 54
factor the polynomial
0= (2w + 9)(w - 6)

Set each set of parentheses equal
to 0 and solve for width.

0=2w+9
-9=2w
-4.5= w NEGATIVE VALUE

0=w-6
6 cm=w

-4.5 is not the answer because it has a negative value. You cannot have a negative side of a photograph. So substitute 6 in to find length.

length= 2w-3
l= 2(6)-3
l= 12-3
l= 9 cm

CHECK:
w= 6cm
l= 9cm
Area= length * width
54= 6*9
54= 54

ANSWER: width= 6cm; length= 9cm

Hope this helps! :)