Question 1166715
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Let x and y be the dimensions of the first rectangle.


We have  xy = 24 for its area.


The dimensions of the second rectangle are (x-4) and (y+1)  with the equation for the area

    (x-4)*(y+1) = 24,  or

    xy + x - 4y - 4 = 24.


Replacing here xy by 24, based on the very first equation, we get

    24 + x - 4y - 4 = 24, 

or, after collecting/canceling common terms

    x - 4y = 4.    (*)


So, we have now two equations

    xy = 24      (1)

    x = 4 + 4y.  (2)


By substituting (2) to (1), you get a quadratic equation

    (4+4y)*y = 24

    (1+y)*y = 6


At this point, you can solve it as a quadratic equation

or GUESS the solution mentally  y = 2.


<U>ANSWER</U>.  The dimensions of the first rectangle are  2 cm (the width)  and  24/2 = 12 cm (the length).
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Solved.