Answer:
We know that this triangle is similar because it will have all of the same angles as the first triangle. This is because two parallel lines cut by a transversal will create the same angles. In addition, they share the final angle because we are not changing that angle. Therefore, all 3 are the same, which makes them similar triangles.
Since J is the midpoint of HK, that means HK is split into two sections HJ and JK that are the same length.
1) You are told that the m<span>easure of segment HJ = 9x-2 and that of segment JK = 4x+13. Since you also know they are equal lengths, you can set these equations equal to each other to find the value of x!
HJ = JK
</span>9x-2 = 4x+13
5x = 15
x = 3
2) Now you know x = 3. Plug that into your given equations for HJ and JK to find the length of each segment (or a shortcut would be to find one of them, and then you also know the other is the same length. I'm doing both, just to make sure I don't make a silly mistake!):
HJ = <span>9x-2
</span>HJ = 9(3) - 2
HJ = 27 - 2
HJ = 25
JK = 4x + 13
JK = 4(3) + 13
JK = 12 + 13
JK = 25
3) Finally, the length of HK is just the length of HJ + JK, or HK = 25 + 25 = 50.
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Answer: HJ = 25, JK = 25, HK = 50
Answer:
5
Step-by-step explanation:
Pythagoras's theorem dictates that a squared + b squared = c squared when talking about sides on right angled triangles with a and b being flat sides and c being the hypotenuse which gives us the forumula below
3 squared + 4 squared = 25 route 25 = 5
T has 4 times what R has, so 2.105*4 which is 8.42
