the sides of a triangle are 15cm 20cm and 21 cm long a line drawn to the side that is 21 cm long bisects the angle opposite that side. how long are the segments into which the side is divided

Answer 1

draw a diagram and use the Triangle Angle Bisector Theorem

the line segment that bisects the angle divides the segment into two segments that are proportional to the other two sides

call the two sides x and 21-x

they are proportional to 20 and 15

x/(21-x)=20/15

simplify the 20/15 if you like

x/(21-x)=4/3

cross multiply

3x=4(21-x)

3x=84-4x

3x+4x=84

7x=84

x=12 and 21-x=21-12=9

the segments are 12 cm and 9 cm