Question

what is the area of the colour square?

Answer 1

Answer:

90 unit^2

Step-by-step explanation:

Notice that ΔCBF is similar to ΔDEF.

     Therefore,

      EF/BF = DF/CF = DE/BC

     5/(5+10) = DF/CF = DE/BC

     1/3 = DF/CF = DE/BC      ...(1)

Let DE = x,  so BC = 3x

Since, ΔACB and ΔEDF are congruent

So, BC = DF = 3x  &        ...(2)

     DE = CA = x

Now,  from (1),  we get DF/CF = 1/3

from (2),  we have DF = 3x

       ∴ 3x/CF = 1/3      ⇒ CF = 9x

&        CF = CD + DF

          9x = CD + 3x

          6x = CD          [side of sq.]

Using Pythagoras theorem in ΔCFB

         CF² + CB² = BF²

         (9x)² + (3x)² = 15²

         81x² + 9x² = 225

        x² = 5/2

Hence,

Area of coloured square = side²

                    = CD²

                    = 36x²

                    = 36(5/2)

                    = 90 unit²