Question

Please help!

What is the value of X?
Enter your answer, as a decimal, in the box. Do you not round your answer.

Answer 1

CD bisects angle C, so makes these ratios proportional:
.. AD/AC = BD/BC
.. 3/4 = x/7.5
.. x = 7.5*(3/4) = 5.625

Answer 2

Angle bisector theorem states that the ratio of the arms of the angle which is bisected is equal to the ratio of the sides intersected by the angle bisector

As CD is the bisector of <ACB

We shall use the angle bisector theorem to find the value of x.

According to the angle bisector theorem

`(AC)/(BC) =(AD)/(BD)`

Substituting the values we get

`(4)/(7.5) =(3)/(x)`

Cross multiplying we get

4x= 3 × 7.5

4x = 22.5

x = 22.5/4

x= 5.625

Hence the value of x shall be 5.625