Question 1207438
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It should be clear that the goal is to reduce the area 12*7 = 84 cm^2 by 10%
by reducing the length of 12 cm to 12-x cm and reducing the width of 7 cm to 7-x cm.


It gives you an equation for the new area

    (12-x)*(7-x) = 0.9*84  cm^2,

or

    (12-x)*(7-x) = 75.6  cm^2


Simplify and reduce this equation to the standard queadratic equation form

    84 - 7x - 12x + x^2 = 78.6

    x^2 - 19x + 5.6 = 0.


Solve using the quadratic formula

    {{{x[1,2]}}} = {{{(19 +- sqrt(19^2 - 4*5.6))/2}}} = {{{(19 +- sqrt(338.6))/2}}} = {{{(19 +- 18.40109)/2}}}.


Thus, one root is  {{{x[1]}}} = {{{(19 + 18.40109)/2}}} = 18.70 cm.

The other root is  {{{x[2]}}} = {{{(19 - 18.40109)/2}}} = 0.299 cm  (rounded).


Obviously, the first root is toooooo big value; so, we deny it.


Check the other root.  The new area is

    (12-0.299)*(7-0.299) = 78.41,


which is close to 78.4 = 0.9*84.


So, our solution is 0.299 cm.


The new dimensions are  12-0.399 = 11.601 cm (the length) and  7-0.399 = 6.601 cm (the width).    <U>ANSWER</U>
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Solved,  with complete explanations.