Question

A city park designer is designing a new park. The park will be shaped like a

right triangle and there will be two pathways for pedestrians, shown by VT
and VW in the diagram. The park planner only wrote two lengths on his
sketch as shown. Based on the diagram, what will be the lengths of the two
pathways?

Answer 1

Part a)
`VW=12\ yd`

Part b)
`VT=9\ yd`

Explanation:

The complete question in the attached figure

we know that

The Triangle Mid-segment Theorem states that:The segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is half the length of that side

step 1

Find out the length of the pathway VW

`VW=(XW)/(2)` -----> by Triangle Mid-segment Theorem

Because V is the midpoint of XY and W is the midpoint of YZ

so

VW is parallel to XW

we have

`XW=24\ yd`

substitute

`VW=(24)/(2)=12\ yd`

step 2

Find the length YZ

Applying the Pythagoras Theorem

`XY^2=XZ^2+YZ^2`

we have

`XY=30\ yd\\XZ=24\ yd`

substitute

`30^2=24^2+YZ^2`

`YZ^2=30^2-24^2`

`YZ^2=324`

`YZ=18\ yd`

step 3

Find out the length of the pathway VT

`VT=(YZ)/(2)` -----> by Triangle Mid-segment Theorem

Because V is the midpoint of XY and T is the midpoint of XZ

so

VT is parallel to YZ

we have

`YZ=18\ yd`

substitute

`VT=(18)/(2)=9\ yd`