Steps
(1) L = 8l + 4h
Re-arrange it into
4h = - 8l + L
h = - 8l/4 +
L/4
h = - 2l +
L/4
(2) Next, draw the line h = - 2l
Use two rulers,
just the way 2 parallel lines are drawn.
Shift the
line h = - 2l in parallel until it just touches the curve h =
8000/l^2
The
interesecting point will be (l, h) = (20,20)
(3) Substitute l = 20 and h = 20
into
h = - 2l +
L/4
20 = - 20(20) +
L/4
80 = - 160 +
L
L = 240
Hence, the smallest value of L is 240
ie the required equation of the line is 240 = 8l +4h
(4) Alternatively, make use of the line that
just touches the curve.
The y-intercept
of this line will be 60.
Since L/4
= 60,
so L = 60
x 4 = 240
Hence, the smallest value of L is
240
ie the required equation of the line is 240 = 8l +4h
The fun part of this question is
that it is not the usual way of questioning in "O" E.Maths curve
graph question ie asking students to find the gradient of the
tangent or to find the co-ordinates of the point where the tangent
and the curve meet.
This question requires the
students to draw the line h = - 2l first and then to move this line
in parallel until it just touches the curve. Next, to make use of
the y-intercept of the line that just touches the curve to find the
smallest value of L.