Question 1191970
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In an isosceles triangle ABC, side AB is twice as long as AC. 
The perimeter of the triangle is 200cm. Find the length of AC. 
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<pre>
Since the triangle is isosceles (given) and since side AB is twice as long as AC,
it means that AC is the base of the triangle, while AB and BC are the lateral sides.


It is only one possible configuration for the triangle to exist.


So, if x is the length of the base AC, then the lateral sides AB and BC have the lengths 2x, each.


Then for the perimeter we have this equation

    AC + AB + BC = 200 cm,

or

    x  + 2x + 2x = 200,

         5x      = 200

          x      = 200/5 = 40.


<U>ANSWER</U>.  The base AC is 40 cm long.  The lateral sides are  2*40 = 80 cm long: they are congruent.
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Solved.