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**mark** this question is particularly tough as don't know how to draw boxes and label them etc but i think it might be able to be done without seeing the boxes, here it is-

a pen is built onto an existing rectangular building where AF is 10 units and FE is 5 units. AF and FE are shared sides between the pen and the rectangular building. the perimeter ABCDE (F is the corner of the rectangular building) is 65 units. find a relationship between x and y where AB = x and DE = y

show that the area enclosed by the pen is $\displaystyle 125 + 30x - x^2$

by completing the square, find the greatest possible area enclosed by the pen.

hats off to anyone that can do this without the visual aid