Question 1089299
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Let w be the width.

Then your equation is

w*(w+8) = (w+4)*((w+8)-5),    or, which is the same,

w*(w+8) = (w+4)*(w+3),

w^2 + 8w = w^2 + 4w + 3w + 12,

w = 12.


<U>Check</U>.  12*(12+8) = 240.

        (12+4)(12+3) = 16*15 = 240.  ! Correct !


<U>Answer</U>.  the original dimensions of the rectangle are 12 x 8 cm.
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Solved.