Question 1149603
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<pre>

Triangles ADE and ABC are similar, and the similarity coefficient is  {{{26/42}}} = {{{13/21}}}.


Let x be the altitude of the triangle ADE;  then the altitude of the triangle ABC is   (x+26) centimeters.


The ratio of altitudes is the same


    {{{x/(x+26)}}} = {{{13/21}}}.


It gives


    21x = 13*(x+26)

    21x = 13x + 13*26

    21x - 13x = 338

     8x       = 338

      x       = 338/8 = 42.25  cm.


Thus the height of the triangle ADE is  42.25 cm;  then its area is  {{{(1/2)*42.25*26}}} = 549.25 cm^2.    <U>ANSWER</U>
</pre>

Solved.