#### Question

# 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

#### Answer

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.

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.

So the answer is a....12.