Given parallelogram SNOW, diagonals SO and NW intersect at D. If SD = 9x+5 and OD = 13X - 3, find the length of SO

The length of SO is 46 units

Step-by-step explanation:

In a parallelogram, diagonals bisect each other, which means meet each other in their mid-point

∵ SNOW is a parallelogram

∵ SO and NW are diagonals

∵ SO ∩ NW at point D

→ That means D is the mid-point of SO and NW

∴ D is the mid-point of SO and NW

∵ D is the mid-point of SO

→ That means D divide SO into two equal parts SD and DO

∴ SD = DO

∵ SD = 9x + 5

∵ DO = 13x - 3

→ Equate them

∴ 13x - 3 = 9x + 5

→ Subtract 9x from both sides

∵ 13x - 9x - 3 = 9x - 9x + 5

∴ 4x - 3 = 5

→ Add 3 to both sides

∵ 4x - 3 + 3 = 5 + 3

∴ 4x = 8

→ Divide both sides by 4

∴ x = 2

→ To find the length of SO substitute the value os x in SD and DO

∵ SO = SD + DO

∵ SD = 9(2) + 5 = 18 + 5 = 23

∵ DO = 13(2) - 3 = 26 - 3 = 23

∴ SO = 23 + 23 = 46

∴ The length of SO is 46 units