Question

If ∆BCD ~ ∆GEF, find the value of x.

Answer 1

x = 13, BD=19

Explanation:

if the triangles are similar then EG/BC = FG/BD

51/(x+4) = 57/(2x-7) cross multiply expressions

102x - 357 = 57x + 228

102x - 57x = 228 + 357

45x = 585 divide both sides by 45

x = 13

BD = 2x -7 and 13×2 - 7 = 19

Answer 2

x = 13

Explanation:

`(x+4)/(51) = (2x-7)/(57)`

(x+4) 57 = (2x-7) 51

57x + 228 = 102x - 357

357+228 = 102x - 57x

585 = 45x

`(585)/(45) = (45x)/(45)`

13 = x or x = 13