Question 1190049
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Let x and y be the dimensions.


Then 

    x + y = 174/2 = 87      (1)    (half the perimeter)

    xy    = 1782            (2)    (the area)


From first equation, express y = 87-x and substitute into the second equation.

You will get single equation for unknown x


    x*(87-x) = 1782,

or

    x^2 - 87x + 1782 = 0.


Solve it using the quadratic formula.


    {{{x[1,2]}}} = {{{(87 +- sqrt((-87)^2 -4*1*1782))/2}}} = {{{(87 +- sqrt(441))/2}}} = {{{(87 +- 21)/2}}}.


Both roots are good,  x= 54 and x= 33.


First root x= 54 determines y = 87-54 = 33;

second root x= 33 determines y = 87-33 = 54.


So, the dimensions of the bakery are 33 and 54 feet.    <U>ANSWER</U>


<U>CHECK</U>  the area:  33*54 = 1782 square feet.   ! Precisely correct !
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Solved.