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a rectangular shaped mansion where the length was 12 more than the square of the width.
If the perimeter of the mansion was 168 meters, what is the measure of its area?'
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If the width is w units, then the length is w^2 + 12 units.
From the info about the perimeter, we have this equation
w + (w^2 + 12) = 168/2,
or
w^2 + w - 72 = 0.
Solve it by factoring
(w+9)*(w-8) = 0.
Then the width is 8 units, and the length is w^2+12 = 8^2+12 = 64+12 = 76 units.
Thus the area of the rectangle is 8*76 = 608 square units. ANSWER
Solved.