Question

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

Answer 1

Answer:

$XY=36\ units$

Step-by-step 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

$AB=\frac{1}{2}YZ$

we have

$AB=24\ units$

substitute

$24=\frac{1}{2}YZ$

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

$BC=\frac{1}{2}XY$ -----> $BC=\frac{1}{2}(36)=18\ units$

$AC=\frac{1}{2}XZ$ -----> $AC=\frac{1}{2}(60)=30\ units$