Question

Each leg of an isosceles triangle is 9 inches

Answer 1

B) 41"
If the legs of 41" are 9" less than half the base, the base is:
(41-9) 2 = 64
All sides of the triangle added together (perimeter):
41" + 41" + 64" = 146"
Hope this helps! ~ArchimedesEleven

Answer 2

Let, the base of the given isosceles triangle be "x"
Now,
If the base is x, then the length of the legs will be $9+ \frac{1}{2}x$
Now, 
Perimeter = sum of all sides
$146 = (9+ \frac{1}{2}x )+(9+ \frac{1}{2}x)+x$

$146 = 18+x+x$

$146 - 18 = 2x$

$128 = 2x$

$\frac{128}{2} =x$

$64 =x$

Now, substitute the value of x in the equation for legs of the triangle,

legs = $9+ \frac{1}{2}x$
     
       = $9+ \frac{1}{2}(64)$
   
       = $9+ 32$
 
       = $41$ inches.

So, the answer to your question is B.