geometry triangles

Question

The sides of a triangle are 15cm, 20cm, and 21cm long. A line drawn to the side that is 21 cm long bisects the angle opposite of that side. How long are the segments in to which the side is divided?

a.) 9 cm, 12 cm

b.) cannot tell

c,) 6 cm, 15cm

d.) 4 cm, 17cm

Answer 1

I had to go look this one up!

The bisector of an interior angle of a triangle divides the opposite side into segments proportional to the adjacent sides.

The proof requires a construction which I did not remember...and you should look it up too.

Once you have that, you get

(15/x) = (20/y) where x and y are the parts of the opposite side.

then (3/4) = (x/y)

add one to each side

(7/4) = (x+y)/y = 21/y

And there is your solution!