XYZ is a right triangle. XY and YZ both equal 5.

1 Answer

• First draw the right Triangle XYZ. XY & YZ are adjacent side containing the right angle and XZ is the hypotenuse (longest side).

  For right triangle sum of squares of sides = square of hypotenuse or

  (XY)^2 + (YZ)^2 = (XZ)^2

  5^2 + 5^2 = XZ^2

  XZ^2= 50 or

  XZ = SQRT(50)

  also W is mid point of large side - then

  XW = 1/2 of XZ or

  XW = .5 SQRT(50)

  Now YWX is a Right triangle. Applying the same sum of squares idendity we have

  (YW)^2 + (XW)^2 = (XY)^2

  (YW)^2 + [.5*SQRT(50)]^2 = 5^2

  (YW)^2 + .25*50 = 25

  (YW)^2 + 12.5 = 25

  Subtracting 12.5 from both sides

  (YW)^2 = 25 - 12.5

  YW = SQRT(12.5) =3.54