Suppose be is an angle bisector of △abc, ab=9, bc=15, and ac=16. find ae and ec.

AE=5 and EC=10

Step-by-step explanation:

Given : Suppose BE is an angle bisector of ΔABC , AB=9, BC=15, and AC=16

To find : AE and EC

Solution : BE form an angle bisector on line AC

Let AE=x and EC = y

Length of AC= AE+EC , putting values

16=x+y .....[1]

Now, we apply angle bisecor theorem which state that the ratio of the length of the line segment AE to the length of segment EC is equal to the ratio of the length of side AB to the length of side AC

Put values,

Cross multiply,

.......[2]

From [1] and [2]

Substitute x from [1] in [2], x= 16-y

Put y in value of x,

x= 16-y

x=16-10=6

Therefore, length of AE=x=5 and EC=y=10

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5.5

step-by-step explanation: