Question

Im confused on the bottom circle answer its a bit weird it reads "a. (use algebra) Use the diagram at the right. What algebraic expression represents GK?

b. if GK = 30, what are GH and JK?"

Answer 1

Explanation:

well you need to add the right expressions for the shorter lines so that there is no overlap. otherwise GK would be too long.

so, how can we combine the 3 red lines to get exactly GK ?

we cannot just add 2 of these lines. the results would always be either too long or too short.

but we see "2x + 3" overlaps a bit with "4x - 3". and hey, the third line "x" is just the length of the overlap of the other 2 lines.

so, we can add the first 2 lines, IF we reduce first one of them by the overlap length.

I picked the second line.

so, we have

2x + 3 - x + 4x - 3 = GK

5x = GK

so, "5x" is the algebraic expression representing GK.

now, if GK = 30, then we know

5x = 30

x = 6

GH = 2x + 3 - x (again, we need to shorten that line by the overlap length to count only to H)

= 2×6 + 3 - 6 = 6 + 3 = 9

JK = GK - GJ = 30 - (2x + 3) (here we need the full line, as we are dealing with J)

= 30 - 2×6 - 3 = 15