Question 855917
<pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
Perhaps this picture will help: 
the 'h' is a 'leg', other leg = 24 (h bisects the base)
hypotenuse = 26
{{{drawing(300,300,   -30,30,-1,12,  
circle(24,0,0.4),
circle(-24,0,0.4),
circle (0, 10,0.4),
line(24,0,0,10),
line(-24,0,0,10),
line(0,0,0,10),
line(-24,0,24,0)
locate (-30, 5, "h")
)}}}
line segment of Height to the base <u>bisects the base</u> (base = 48)
Therefore: 26^2 - 24^2 = h^2 = 100, h = 10
 A = {{{(1/2)48*10}}} = 240
 Find the base of the other triangle 
 A = 240 = {{{(1/2)b*sqrt(26^2 - (b/2)^2)}}}
    480= {{{b*sqrt(26^2 - (b/2)^2)}}}
    480^2/b^2 = 26^2 - (b^2/4
    b^4  -4(26^2)b^2 + 4(480^2)  Let x = b^2
    x^2 - 2704x + - 921600
x = 400 0r x = 2304
 b = 20  0r b = 48
the base of the other triangle is 20
CHECKING our answer***
 26^2 -10^2 = 576= h^2,   h = 24   AND  {{{A = (1/2)20*24 = 240}}}
Wish You the Best in your Studies.