MHB Calculating the Length of BC: A Geometric Exploration

[Albert1]

Find length of BC:

View attachment 708

 

[caffeinemachine]

Find length of BC:

View attachment 708

Hello Albert,

In the above problem can you please clarify if E lies on BC or not? If not, then how is E defined other than than AE=10.

 

[Albert1]

Point E is on angle bisector of angle A, and AE=10

E is not on BC (from the diagram given)

 

[caffeinemachine]

Point E is on angle bisector of angle A, and AE=10

E is not on BC (from the diagram given)

But then I think BC doesn't have a unique length. Take BC =16 and the mid point of BC be D. Point E is on the side of BC different from that of A and ED=2 with ED perpendicular to BC. In fact any value of BC>16 can provide a configuration confirming to the hypothesis if the question.

 

[Albert1]

yes, the length of BC is not unique ,it depends on how student draw the diagram

sometimes we plot an open problem ,and want to test the abilities of students in analyzing

now using the diagram given if I said BC=$\dfrac {50}{3}$

what wiil be the sum of the three side lengths of triangle ABC ?

 

[caffeinemachine]

yes, the length of BC is not unique ,it depends on how student draw the diagram

sometimes we plot an open problem ,and want to test the abilities of students in analyzing

now using the diagram given if I said BC=$\dfrac {50}{3}$

what wiil be the sum of the three side lengths of triangle ABC ?

$10$ and $40/3$. Is this correct?

 

[Albert1]

yes,you got it :)