Question

In given fig ∆abc is similar to triangle xyz and ad and xe are angke bisector of a and d such that ad=4 and xe=3cm. Resp find the ratio of abc and xyz

Answer 1

In triangle ABD and triangle XYE

angle B = angle Y (because ∆ABC is similar to ∆XYZ)

Now, angle A = angle X (because ∆ABC is similar to ∆XYZ)

angle BAD = angle YXE = 1/2 of angle A and angle X

Therefore because ∆ABD is similar to ∆XYE by AA similarity criterion

AB/XY = BD/YE = AD/XE

AB/XY = AD/XE --------(1)

Now, we know that ratio of areas of two similar triangles is equal to the ratio of the square of their corresponding sides.

ar∆ABC/ar∆XYZ = AB^2/XY^2

From (1)

ar∆ABC/ar∆XYZ = AD^2/XE^2

ar∆ABC/ar∆XYZ = 4^2/3^2

= 16:9