Question

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?

Answer 1

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