FINDING MISSING LENGTH USING ANGLE BISECTOR THEOREM

If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the other two sides.

bisecthe

Find the missing length indicated.

Problem 1 :

bisectheq1

Solution:

Let missing length to be x.

21=4x2x=4x=2

Problem 2 :

bisectheq2

Solution:

Let missing length to be x.

156=x86x=120x=20

Problem 3 :

bisectheq3

Solution:

Let missing length to be x.

12x=162816x=336x=21

Problem 4 :

bisectheq4

Solution:

Let missing length to be x.

4x=12912x=36x=3

Problem 5 :

bisectheq5

Solution:

Let missing length to be x.

33-x=9618=9(3-x)18=27-9x9x=27-189x=9x=1

So, 3 + 1 = 4

Problem 6 :

bisectheq6

Solution:

Let missing length to be x.

66-x=12848=12(6-x)48=72-12x12x=72-4812x=24x=2

So, 6 + 2 = 8

Problem 7 :

bisectheq7

Solution:

Let missing length to be x.

x-44=211212(x-4)=8412x-48=8412x=84+4812x=132x=11

So, 11 + 4 = 15

Problem 8 :

bisectheq8

Solution:

Let missing length to be x.

x-99=101515(x-9)=9015x-135=9015x=90+13515x=225x=15

So, 9 + 15 = 24

Problem 9 :

Find the value of x.

bisectheq9

Solution:

2115=14x21x=210x=10

Problem 10 :

Find the value of x.

bisectheq10
13x=715-x7x=13(15-x)7x=195-13x20x=195x=9.75

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