SOLUTION: Triangle ABC below is isosceles, with AB=AC. A square is inscribed in the triangle, with edges 26cm, and BC=42cm. Find the area, in cm2, of triangle ADE. Diagram: https://imgur

Algebra ->  Surface-area -> SOLUTION: Triangle ABC below is isosceles, with AB=AC. A square is inscribed in the triangle, with edges 26cm, and BC=42cm. Find the area, in cm2, of triangle ADE. Diagram: https://imgur      Log On


   

Question 1149603: Triangle ABC below is isosceles, with AB=AC. A square is inscribed in the triangle, with edges 26cm, and BC=42cm. Find the area, in cm2, of triangle ADE.
Diagram: https://imgur.com/a/uFHAhYO
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Triangles ADE and ABC are similar, and the similarity coefficient is  26%2F42 = 13%2F21.


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%2F%28x%2B26%29 = 13%2F21.


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  %281%2F2%29%2A42.25%2A26 = 549.25 cm^2.    ANSWER

Solved.