In triangle ABC, B = 90 degrees, AB = 25, and BC = 50. If DBEF is a square, find the area of square DBEF.
+128473 We have two similar triangles here....
Triangle ADF is similar to triangle ABC
And this means that
AD / DF = AB /BC
AD/ DF = 25 / 50
AD/ DF = 1/ 2
But since DBEF is a square.....then BD = DF
So
AD / BD= 1/2 ⇒ AD : BD = 1 : 2
Which means that BD = 2/3 of AB = (2/3)(25)
Then the area of DBEF = BD^2 = [ (2/3) (25) ]^2 = (4/9)(625) = 2500/9 units^2
