Question

Convex quadrilateral ABCD has AB = 9 and CD = 12. Diagonals AC and BD intersect at E, AC = 14.
and triangleAED and triangle BEC have equal areas. What is AE? ​

Answer 1

Answer:

6

Step-by-step explanation:

Given  

Convex quadrilateral ABCD has AB = 9 and CD = 12. Diagonals AC and BD intersect at E, AC = 14.and triangle AED and triangle BEC  

By using sine formula we get for Δ AED and  BEC,

Wee see angle AED = BEC

AE x ED = BE x EC

AE/EC = BE/ED

Since angle AEB = angle DEC, Δles AEB and DEC are similar.

So AB/CD = ¾ since AE + EC = 14

Now EC = 8 and AE will be equal to 6

So AE = 6

         OR

AEB and CED are similar triangles

Area of AED and BEC are equal and angle EAB = angle CED (opposite angles)

Now let AE = x and EC = 14 – x (using similarity)

So x/9 = 14 – x / 12

12 x = 9(14 – x)

12 x = 126 – 9x

21x = 126

So x = 6