The sides of an isosceles triangle have lengths 2x + 4, x + 8. The base has length 5x − 2. What is the length of the base?

Question

hartnn · Answer

so you know that the 2 sides in an isosceles triangle are equal?

so we can do,
$2x+4 = x+8$
Try to find x from this?

anonymous · Answer

x= 4

hartnn · Answer

thats correct! :)

now just plug x = 4 in 5x-2

$5(4) - 2 = ..?$

that would be the length ofbase.

anonymous · Answer

thanks ;)

hartnn · Answer

welcome ^_^

anonymous · Answer

Two sides of an isosceles triangle are  equal.

Using the above statement I may form the following equation:
2x + 4 = x + 8

Now subtract x on both sides

i.e,
$$2x - x + 4 = x + 8 - x$$

Now,

2x - x comes down to just x so the LHS is :
x+4 

For the RHS , - x cancels out + x

Therefore,
RHS = 8

Now equate the new LHS to the new RHS

that is:

x + 4 = 8

This time subtract 4 on both sides.
Again, by repeat the above steps 
i.e,

$$x + 4 - 4 = 8- 4$$

hartnn · Answer

nice explanation @MatthewPFDS  :)

anonymous · Answer

It seems someone else already explained it to you..

and thanks @hartnn  :)