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Algebra II Parabola Challenge Problem. Due Friday October 31st. Boo.
The boundary of a lot of land is called the property line. Many communities do not allow you to
build right up to the property line. Zoning laws may require a “setback” of several feet to
ensure some distance between buildings and between a building and the property line.
Suppose the setback for a building is ‘s’ ft on all four sides of a lot that has width 50 feet and
length 60 feet.
a) Write an expression for the max width in terms of s . Hint lets say ‘s’ is 5ft. Then the width is 50 –
2(5) = 40
b) Write an expression for the max length in terms of s.
c) What is the area of the ENTIRE lot?
e) Write an expression for the area of the building in terms of s.
f) What is the minimum area NOT occupied by the base of the building when s = 6ft?
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g) Suppose the maximum area of the base of the building is 2376ft. What is the value of the
setback?
h) Suppose the minimum area that is NOT occupied by the building is 1344ft. What is the value
of the setback?
i) Write an equation for the perimeter of the building in terms of s.
j) Suppose the lot is 30ft by 90ft. The setback is ‘s’ ft. Write an expression for the maximum
area of the base of the building.