Question

Please answer the 5th question

Answer 1

Since ABC is a right angled triangle,

therefore, AC^2 = AB^2 + BC^2 (Pythagoras thereom)

AC^2 = BC^2 + BC^2 (Since angles are equal in an isosceles triangle, the opposite sides are also equal)

AC^2 = 2BC^2 - (i)

Now in AEC and BDC,

All angles are equal to 30 degrees (because both are equi. triangles)

thus AEC is similar to BDC (by AAA test or AA test)

ar(AEC)/ar(BDC) = AC^2/BC^2

= 2BC^2/BC^2 (From (i))

= 2

hence ar(BDC) = ar(ACE)/2