# In triangle ABC above, what is the length of side BC?

Good Afternoon,

I am having problems understand this geometry problem and was hoping someone could help me with it. Here is the link to the image:

http://i42.photobucket.com/albums/e319/tomh68/HOMEWORK/abcbctriangle.jpg

The question is:

In triangle ABC above, what is the length of side BC?

a) 12

b) 13

c) 14

d) 15

e) 16

I really don't even know where to start to figure out the length of this? Can someone show me how?

Hope to hear from someone soon.

Sincerely,

arted

Let the perpendicular on to BC meet BC at M, say. Then BC = BM + MC.

Triangle AMC has one right-angle, and one of 45o, so the other angle is also 45o. This means that the sides AM and MC are of equal length. So length of MC = 8 .

Triangle AMB is also right-angled, with one side of length 8, and a hypotenuse of length 10. So the length of BM = √(100 - 64) = 6.

Hence BC = BM + MC = 6 + 8 = 14.

Jul 28 at 7:36

Use the pythagoreum Theorum

10^2-8^2=c^2

100-64=c^2

36=c^2

c=6

BC is twice the lenght of the side we just calculated.