Question 78031
The base of an isosceles triangle is 14 in. less than the length of the equal sides. If the perimeter of the triangle is 43 in., find the length of each of the sides. 
Hint: An isosceles triangle has 2 sides of equal length. The third side is different.
Hint: To find the perimeter of a triangle, add all 3 sides.
Hint: Be sure to check your answer. Do all three sides add up? 
Answer: The length of the three sides of the triangle are ________ inches, ________ inches, and __________ inches.
<pre><font size = 5><b>
Draw the isosceles triangle:

    /\
   /  \
  /    \
 /      \
/________\
   
Let each of the equal sides be x. Put "x"
on each of them, like this

    /\
   /  \
 x/    \x
 /      \
/________\
   
Then read what the problem says about the
base in the first sentence:

>>...The base...is 14 in. less than the length 
     of the equal sides...<< 

So we start with the length of the equal sides,
which is x, and then subtract 14, so we have x-14
for the base. So we write "x-14" on the base, like
this:

    /\
   /  \
 x/    \x
 /      \
/________\
   x-14

Now we look through the problem to see what we 
haven't used, and we find:

>>...the perimeter of the triangle is 43 in...<<

Perimeter means "distance all the way around"
That is, it means "sum of all sides". This means 
if we add all three sides we have to have
som,ething which equals 43. So we make our 
equation:

Left side + Right side + Bottom side = 43
     <font face = "symbol">¯</font>           <font face = "symbol">¯</font>           <font face = "symbol">¯</font>          <font face = "symbol">¯</font>  
     x    +      x     +    x-14     = 43

or
                      x + x + x - 14 = 43

                             3x - 14 = 43

Solve that and get x = 19.  So each of the
equal sides is 19 inches long.

The base is 14 less than that, and since
19 - 14 = 5, the base is 5 inches long.

Now let's check to see if the perimeter is
43:

Left side + Right side + Bottom side = 43
     <font face = "symbol">¯</font>           <font face = "symbol">¯</font>           <font face = "symbol">¯</font>          <font face = "symbol">¯</font>  
    19    +     19     +     5     =   43

Yes the 3 sides do indeed add up to 43.

Edwin</pre>