Question 866876
Base of b, for the isosceles triangle, two equal sides 10; and altitude h.  The altitude forms two right triangles each of base b/2 and hypotenuse 10.  Difficult to draw on this site system, so draw this on paper yourself to see. 


This is not the complete solution, but most of the way to get to it.


Pythagorean theorem lets you use b/2 and the hypotenuse 10, to get h, the altitude.  
{{{h^2+(b/2)^2=10^2}}}
{{{h^2=100-(b/2)^2}}}
{{{h=sqrt(100-b^2/4)}}}
h=...
{{{h=(1/2)sqrt(400-b^2)}}}
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Using {{{A=(1/2)b*h}}} in general, b is the base of the isosceles triangle
want {{{(1/2)b*(1/2)sqrt(400-b^2)<48}}} as specified.
{{{(1/4)b*sqrt(400-b^2)<48}}}
{{{highlight_green(b*sqrt(400-b^2)<192)}}}, important rule about the base of this isosceles triangle.


This limit on b will be somewhere around 12, based on using a graphing tool.