closing off first quadrant

You are planning to close off the corner of the first quadrant with a line segment 20 units long running from (a,0) to (0,b). Show that the area of the triangle enclosed by the segment is largest when a=b

From applications of derivatives...this is really tough!!

Write the equation that relates a to b:
a^2 + b^2 = 20^2 = 400
Now differentiate with respect to a, with b as a function of a.
2 a + 2 b db/da = 0
db/da = -(a/b)

Area = a b/2
Call the area A
dA/da = 0 at maximum
b + a db/da = 0
b + a (-a/b) = 0
a^2/b = ba^2 = b^2
Therefore a = b, since both are positive

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asked by Jen
  1. a line through ( 0,13) is 5 units from the origin in quadrant 1. find the equation.


    please help me thanks!

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    posted by Jane

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