if ABC is similar to XYZ and AD and XEare angle bisectors of angle A and angle X respectively such - Maths - Triangles

Question

if ABC is similar to XYZ and AD and XEare angle bisectors of angle
A and angle X respectively such that AD AND XEin cms are 4 and 3
respectively,find area of triangle ABD AND XYE

Ashutosh Verma · Accepted Answer

Answer :

We form our diagram from given information , As :
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_55b304b92bf05%20jpg"
style="width: 519px; height: 187px;">
Here triangle ABC is similar to triangle XYZ , and AD and XE are
angle bisectors of angles A and X respectively , So

Since, ∆ABC ~ ∆XYZ, then∠A = ∠X  corresponding angles of similar ∆'s are equal∠B = ∠Y  corresponding angles of similar ∆'s are equal∠C = ∠Z  corresponding angles of similar ∆'s are equalNow, ∠A= ∠X⇒12∠A = 12∠X⇒∠BAD = ∠YXEIn ∆ABD and ∆XYE,∠B = ∠Y  Given∠BAD = ∠YXE  given∆ABD ~ ∆XYE  AAWe know that ratio of areas of 2 similar ∆'s is equal to the square of the ratio of corresponding sides

⇒Area of ∆ ABDArea of ∆ XYE = AD2XE2⇒Area of ∆ ABDArea of ∆ XYE = 4232⇒Area of ∆ ABDArea of ∆ XYE = 169          ( Ans )

if ABC is similar to XYZ and AD and XEare angle bisectors of angle A and angle X respectively such that AD AND XEin cms are 4 and 3 respectively,find area of triangle ABD AND XYE.