The question is incomplete, here is a complete question.
Triangle FGH is an isosceles right triangle with a hypotenuse that measures 16 units. An altitude, GJ, is drawn from the right angle to the hypotenuse.
What is the length of GJ?
A. 2 units
B. 4 units
C. 6 units
D. 8 units
Answer : The correct option is, (D) 8 units
Step-by-step explanation :
Given:
Length FH = 16 unit
As we know that a altitude between the two equal legs of an isosceles triangle creates right angles is a angle and opposite side bisector.
Thus,
Length FJ = Length HJ = = 8 units
As, the triangle is an isosceles. So, length GF = length GH = x unit
First we have to determine the value of 'x'.
Using Pythagoras theorem in ΔFGH :
Now put all the values in the above expression, we get :
Thus, length GF = length GH = x unit =
Now we have to determine the length GJ.
Using Pythagoras theorem in ΔGJH :
Now put all the values in the above expression, we get :
Thus, the length of GJ is, 8 units.