Question

Security fence encloses a rectangular area on one side of a park in a city. three sides of fencing are​ used, since the fourth side of the area is formed by a building. the enclosed area measures 1682 square feet. exactly 116 feet of fencing is used to fence in three sides of this rectangle. what are the possible dimensions that could have been used to construct this​ area?

Answer 1

Hi,
Let assume a the width and b the length of the rectangular area.
$\left \{ {{2a+b=116} \atop {a*b=1682}} \right. \\\\ \left \{ {{b=116-2a} \atop {a*(116-2a)=1682}} \right. \\\\ \left \{ {{b=116-2a} \atop {a^2-58a+841=0}} \right. \\\\ \left \{ {{b=116-2a} \atop {(a-29)^2=0}} \right. \\\\ \left \{ {{a=29} \atop {b=116-2*29}} \right. \\\\ \left \{ {{a=29} \atop {b=58}} \right.$