Question

All help is much appreciated please and thank you

Answer 1

Once again the traingles are similar by ASA similarity creteria.

So,
HG/KH = HI/HJ = GI/KJ

Now,
Since GI divides the two sides in two equal parts,

KH = HG
and
HI =HJ

the ratio of sides HG/ KH = HG / 2HG = 1/2.

Now,


`(GI)/(KJ ) = (1)/(2) \\ \\ (x - 69)/(x - 42) = (1)/(2) \\ \\ 2x - 138 = x - 42 \\ \\ x = - 42 + 138 = 96`

Therefore x = 96 units.

Answer 2

x = 96

Explanation:

Since GI is a midsegment then it is one half the measure of JK, that is

JK = 2GI, that is

x - 42 = 2(x - 69) ← distribute

x - 42 = 2x - 138 ( subtract x from both sides )

- 42 = x - 138 ( add 138 to both sides )

96 = x