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

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(52782) (Show Source): You can put this solution on YOUR website!
.


Triangles ADE and ABC are similar, and the similarity coefficient is   = .


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


     = .


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   = 549.25 cm^2.    ANSWER

Solved.

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