In ABC, O is the centroid of the triangle and AO is 12.7 m. Find the length of OY and AY.
Accepted Solution
A:
Answer:[tex]\boxed{OY = 6.35 m} \\\boxed{AY=19.05 m}[/tex]Step-by-step explanation:The centroid of a triangle always cuts a triangle perfectly at 2/3. What I mean by this is that the line that touches the tip of the triangle and touches the median of the base is cut into one third and its other part is cut into two thirds of the whole segment. This segment is AY. Knowing this, I can tell that OY is 1/3 of the length of AO, which is given to be 12.7 m.To find OY, make an equation where AO and OY add up to AY.[tex]12.7+\frac{1}{3} x=x[/tex]The variable x represents the length of AY, and 1/3x represents the length of OY (because it is one-third of AY).Solve the equation by subtracting 1/3x from both sides.[tex]12.7=\frac{2}{3} x[/tex]Divide both sides by 2/3.[tex]x=19.05[/tex]Now we know the length of AY (x). To find the length of OY substitute this value of x into 1/3x, which represents OY.[tex]\frac{1}{3} (19.05)[/tex]This gives us 6.35, which is the length of OY.The final answers are:OY = 6.35 mAY = 19.05 m