Question

A, B, and C are midpoints of ∆XYZ. What is the length of cy

Answer 1

48

Explanation:

got it right on gradpoint :)

Answer 2

`XY=36\ units`

Explanation:

The correct question is

A, B, and C are midpoints of ∆XYZ. What is the length of XY

we know that

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side

step 1

Find the length of YZ

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

we have

`AB=24\ units`

substitute

`24=(1)/(2)YZ`

solve for YZ

`YZ=48\ units`

step 2

Find the length of XY

Applying Pythagoras Theorem in the right triangle XYZ

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

substitute the given values

`60^2=XY^2+48^2`

solve for XY

`3,600=XY^2+2,304`

`XY^2=3,600-2,304`

`XY^2=1,296`

`XY=36\ units`

Applying the Midpoint Theorem

`BC=(1)/(2)XY` ----->
`BC=(1)/(2)(36)=18\ units`

`AC=(1)/(2)XZ` ----->
`AC=(1)/(2)(60)=30\ units`