In the diagram below, EU = 8, UF = 7,GV = 5, VH = 16, and UV= 8. Find XY.
+23253 HInts:
1) XU · UY = UF · UE ---> XU · UY = 56
GV · VH = XV · VY ---> XV · VY = 80
2) UY = UV + VY
XV = XU + UV
3) Combining 1) and 2): XU · UY = 56 ---> XU · (UV + VY) = 56
HV · VY = 80 ---> (XU + UY) · VY = 80
4) To make the notation simpler: x = XU and y = VY
5) So: x · (8 + y) = 56 ---> x = 56 / (8 + y)
(x + 8) · y = 80 ---> x = 80 / y - 8
6) Combining these two equations: 56 / (8 + y) = 80 / y - 8
Multiply each term by the least common denominator and solve, using the quadratic formula.
7) So: x · (8 + y) = 56 ---> y = 56 / x - 8
(x + 8) · y = 80 ---> y = 80 / (x + 8)
8) Combine the two equations of step 7) and solve in a way similar to how step 6) was solved.
9) You now have the values for x and y and you know the value of UV; add.
10) The answer isn't 24.
