Answer:
Explanation:
8) triangle DGH is similar to triangle DEF.
DG/DE = GH/EF
52/91 = (x + 3)/(2x - 1)
52(2x - 1) = 91(x + 3)
104x - 52 = 91x + 273
104x - 91x = 273 + 52
13x = 325
x = 325/13
x = 25
9) ∆XYZ is similar to ∆RST
XY/RS = YZ/ST = XZ/RT
(5x - 3)/(3x + 2) = 60/40
40(5x - 3) = 60(3x + 2)
200x - 120 = 180x + 120
200x - 180x = 120 + 120
20x = 240
x = 240/20
x = 12
10) ∆ABC is similar to ∆ EDC
AB/ED = BC/DC = AC/EC
(3x - 5)/32 = (5x - 5)/56
56(3x - 5) = 32(5x - 5)
168x - 280 = 160x - 160
168x - 160 = - 160 + 280
8x = 120
x = 120/8
x = 15
11) ∆JKL is similar to ∆MKN
JK/MK = KL /KN = JL/MN
32/12 = (3x - 2)/(x + 1)
32(x + 1) = 12(3x - 2)
32x + 32 = 36x - 24
36x - 32x = 32 + 24
4x = 56
x = 56/4
x = 14
12) ∆BCD is similar to ∆GEF
(x + 4)/51 = (2x - 7)/57
57(x + 4) = 51(2x - 7)
57x + 228 = 102x - 357
102x - 57x = 228 + 357
45x = 585
x = 585/45
x = 13