A triangle has two equal sides 4 inches long. what is the length of the third side (the base) if the triangle is to have maximum area?

Question

2647 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-01T23:57:04

#4sqrt(2)# inches

Suppose the base is of length #x# inches.

Using Pythgoras, the height of the triangle is:

#sqrt(4^2-(x/2)^2)#

So the area of the triangle is:

#a(x) = 1/2 xx "base" xx "height" = 1/2 x sqrt(4^2-(x/2)^2)#

then #16(a(x))^2 = 64x^2-x^4= 1024-(x^2-32)^2#

This will have its maximum value when #x^2-32 = 0#, that is when #x = +-sqrt(32) = +-4sqrt(2)#.

Since we are dealing with lengths, which must be non-negative, we can deduce that #x = 4sqrt(2)#