Draw the rectangle and its diagonal, putting
the length  on the diagonal:



Label the width .

Since the length is 3 cm longer than the width,

label the length 



Erase the upper left half of the rectangle:



That leaves a right triangle, with legs 

 and hypotenuse .

So we use the Pythagorean theorem:

 with 















Divide through by 2:





Think of two integers which
have product -108 and combine
to give +3:

They are -9 and +12, so the
left sides factors as:



Use the zero-factor principle



We choose the positive value for the width,

Therefore the width = 9cm
and the length = w+3 = 9+3 = 12cm

Edwin