10. a) This question is indeed a little tricky and requires us to work through a few steps to find the value of GK.
So, first of all, you should be able to notice that the value of GK is the sum of the values of GH, HJ and JK (or this can be written as the sum of GH and HK, or GJ and JK).
In the diagram itself, we are given that:
GJ = 2x + 3
HJ = x
HK = 4x - 3
Now, there are actually a few ways to go about solving this, but I will show you how to find the value of GH, which we can then add to HK to get the value of GK.
Looking at the diagram, if we wanted to find the value of GH, we could take the value of GJ and subtract the value of HJ. Thus:
GH = GJ - HJ
GH = 2x + 3 - x
GH = x + 3
Now, given that GK = GH + HK, we can get:
GK = GH + HK
GK = (x + 3) + (4x - 3)
GK = 5x
Thus, the value of GK is 5x.
b) This question asks us to find the values of GH and JK if GK = 30.
Again, there are a few methods of doing this, however we will first substitute GK = 30 into GK = 5x to find the value of x:
30 = 5x
x = 6
Now, in 10. a), we have already found that the value of GH is x + 3. Thus, substituting in x = 6, we get:
GH = x + 3
GH = 6 + 3
GH = 9
The value of JK may be given by the value of GK minus the value of GJ:
JK = GK - GJ
JK = 30 - (2x + 3)
JK = 30 - (2*6 + 3)
JK = 30 - (12 + 3)
JK = 30 - 15
JK = 15
Thus, if GK = 30, GH = 9 and JK = 15.
Hope that helped, but if you have any further questions please feel free to comment below :)
