# 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?

##### 1 Answer

Nov 1, 2015

#### Explanation:

Suppose the base is of length

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

This will have its maximum value when

Since we are dealing with lengths, which must be non-negative, we can deduce that