Question

In the diagram, E is the centroid of ABC. AD = 7.5 centimeters, AD BC and AE BD.

Answer 1

Determine the length of side AE.

`\begin{gathered} AE=(2)/(3)AD \\ =(2)/(3)\cdot7.5 \\ =5 \end{gathered}`

So length of side BD is equal to 5 cm.

Determine the length of side AB.

`\begin{gathered} (AB)^2=(7.5)^2+(5)^2 \\ =56.25+25 \\ =81.25 \\ AB=\sqrt[]{81.25} \\ \approx9.01 \end{gathered}`

The length of side AB and AC is equal so,

`AC=9.01`

Determine the perimeter of triangle.

`\begin{gathered} P=2\cdot5+9.01+9.01 \\ =10+18.02 \\ =28.02 \end{gathered}`

So perimeter of triangle is equal to 28.02 cm.