Question

1. Calculate what should be written instead of question marks.

Answer 1

To find:

The values of the unknowns.

Solution:

It is known that in a triangle, the centroid divides each median in the ratio of 2:1.

a)

In the first triangle, we have OC : OE = 2:1. So,

`\begin{gathered} (OC)/(OE)=(2)/(1) \\ (5)/(OE)=2 \\ OE=2.5\text{ cm} \end{gathered}`

And AO : OF = 2:1. SO,

`\begin{gathered} (AO)/(OF)=(2)/(1) \\ (6)/(OF)=2 \\ OF=3\text{ cm} \end{gathered}`

And BO : OD = 2:1. So,

`\begin{gathered} (BO)/(OD)=(2)/(1) \\ (BO)/(2)=2 \\ BO=4\text{ cm} \end{gathered}`

Thus, we get BO = 4 cm, OF = 3 cm, EO = 2.5 cm.

b)

In the second triangle, given that AE = 10 cm, DO = 3 cm. Since the centroid divides each median in the ratio of 2:1. SO,

`\begin{gathered} (AO)/(OE)=(2)/(1) \\ (AO)/(AE-AO)=2 \\ (AO)/(10-AO)=2 \\ AO=20-2AO \\ 3AO=20 \\ AO=(20)/(3) \end{gathered}`

And OC : DO = 2:1. SO,

`\begin{gathered} (OC)/(DO)=(2)/(1) \\ (DC-DO)/(DO)=2 \\ (DC-3)/(3)=2 \\ DC-3=6 \\ DC=9\text{ cm} \end{gathered}`

Thus, DC = 9 cm, AO = 20/3 cm.