Question

In the figure below, points J, K, and L are the midpoints of the sides of AXYZ. Suppose XZ=28, KL = 42, and YZ = 76. Find the following lengths.

Answer 1

Given data:

The first length is XZ=28.

The second length is KL = 42.

The third side of triangle is YZ = 76.

If line passing through the mid points of the two sides of the triangle then the given line is half of the third side.

`\begin{gathered} KL=(1)/(2)XY \\ XY=2(KL) \end{gathered}`

Substitute the given value in the above expression.

`\begin{gathered} XY=2(42) \\ =84 \end{gathered}`

The expression for JY is,

`JY=(1)/(2)XY`

Substitute 84 for XY in the above expression.

`\begin{gathered} JY=(1)/(2)(84) \\ =42 \end{gathered}`

The expression for JK is,

`JK=(1)/(2)(YZ)`

Substitute 76 for YZ in the above expression.

`\begin{gathered} JK=(1)/(2)(76) \\ =38 \end{gathered}`

Thus, the value of XY is 84, the value of JY is 42, and the value of JK is 38.