A new fence is constructed on three sides of a housing block with area 240 m2. the fourth side facing the road is left open. if 52 m of fencing is used, what are the dimensions of the block?

Suppose the side parallel to the open side be y m and each of the other two sides be x m

thus

2x+y=52

hence

y=52-2x

area is given by:

area=xy

x (52-2x) = 240

re-writing the above we get

-2x^2+52x-240=0

x^2-26x+120=0

factoring the above we get:

(x-20) (x-6) = 0

thus

x=20 or x=6

if x=20, then y=52-40=12

if x=6, then y=52-12=40