Answer:
For the first question, x = 12.
For the second question, x = -9
Step-by-step explanation:
In the first question, in △RSQ,
RZ/RS = 1/2 = RY/RQ (given)
∠ZRY = ∠ZRY (common)
∴ △RZY ~ △RSQ (2 sides prop., inc. ∠)
∵ △RZY ~ △RSQ
∴ RZ/RS = RY/RQ = ZY/SQ = 1/2
(x+2) / (3x-8) = 1/2
2(x+2) = (3x-8)
2x + 4 = 3x - 8
3x - 2x = 12
x = 12
In the second question, in △SRT,
SC/SR = 1/2 = SB/ST (given)
∠CSB = ∠CSB (common)
∴ △SCB ~ △SRT (2 sides prop., inc. ∠)
∵ △SCB ~ △SRT
∴ SC/SR = SB/ST = CB/RT = 1/2
(x+19) / (x+29) = 1/2
2(x+19) = (x+29)
2x + 38 = x + 29
2x - x = 29 - 38
x = -9
Hope this helped!
