Question

100 POINTS! PLEASE HELP!

Answer 1

Answer:

1. x=5. 2. x=3

Step-by-step explanation:

Ok, so I actually spent 2 hours doing the first problem, I considered the angles to be different at first, i will add my messy work if you are interested haha.

However, I realized that the only way this question can be possible to solve is if the angles are equal, and there is no information given to say that they are different (they are both indicated by one line, while angles that are different are usually represented with multiple lines).

The general method for such problems is to consider the ratio of the sides to the side lengths into which the long side is divided.

For the first picture, the answer can be found by: 9/(2x-1) = 15/(3x). From here, we find that x = 5 (do some algebra). I actually got the same answer when doing this problem with the sine rule.

I am only looking now at the second problem, and i can tell straight away that we can get the solution by solving 3/2.25 = 4/x. x = 3 after some algebraic manipulation.

So yeah, this was a not so fun experience of trying to do this problem without knowing the angles were equal, but i learned a lot haha :)

PS. I am only adding my terrible working out because i hate myself for being so silly

Answer 2

Answer:

• x = 5 and x = 3

Step-by-step explanation:

Use of angle bisector theorem:

• An angle bisector in a triangle divides the opposite side into two segments which are in the same proportion as the other two sides of the triangle.

#1

• AB / AC = (2x - 1) / 3x
• 9 / 15 =  (2x - 1) / 3x
• 9(3x) = 15(2x - 1)
• 27x = 30x - 15
• 30x - 27x = 15
• 3x = 15
• x = 5

#2

• AC / CB = AD / BD
• 3/4 = 2.25 / x
• 3x = 4*2.25
• 3x = 9
• x = 3