Question

8,9,10,11 and 12?? Geometry homework

Answer 1

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