In the diagram below, EU = 8, UF = 7, GV = 5, VH = 8, and UV = 6. Find XY.
+128458 We have that
EU * UF = XU * UY
EU * UF = XU (UV + VY)
8 * 7 = XU ( 6 + VY)
56 = XU (6 + VY)
56 / (6 + VY) = XU (1)
Also
GV * VH = XY * VY
GV * VH = (XU + UV) * VY
5 * 8 = ( XU + 6) * VY sub in (1) for XU
40 = [ 56 / (6 + VY) + 6 ] * VY
Let VY = x
40 = [ 56 / (6 + x) + 6 ] * x
40 = [ 56 + 36 + 6x ] * x / ( 6 + x)
40 (6 + x) = [ 92 + 6x ] * x
240 + 40x = 92x + 6x^2
6x^2 + 52x - 240 = 0
Using the quadratic formula produces the positive value of x = 10/3 = VY
So XU = 56 / ( 6 +10/3) = 6
So
XY = XU + UV + VY = 6 + 6 + 10/3 = 46 / 3
