Myres245
Answered

Each leg of an isosceles triangle is 9 inches

longer than one-half the length of the base. If

the perimeter of the isosceles triangle is

146 inches, what is the length of one leg of the

isosceles triangle?

A 64 in.

B 41 in.

C 50 in.

D 82 in.

Verified Answer :

ArchimedesEleven

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

rabinshrestha41

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.


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