Triangle FGH is an isosceles right triangle with a hypotenuse that measures 16 units. An altitude, overline (GJ), is drawn from the right angle to the hypotenuse. What is the length of overline (GJ') 2 units 4 units 6 units 8 units

To find the length of $\overline{GJ}$, we can use the Pythagorean theorem.<br /><br />Step 1: Let's label the sides of the triangle. We have:<br />- Hypotenuse (FG) = 16 units<br />- Leg (FH) = x units<br />- Leg (GH) = y units<br /><br />Step 2: According to the Pythagorean theorem, we have:<br />$FG^2 = FH^2 + GH^2$<br />$16^2 = x^2 + y^2$<br />$256 = x^2 + y^2$<br /><br />Step 3: Since triangle FGH is an isosceles right triangle, we know that $x = y$. So we can substitute $y$ with $x$ in the equation:<br />$256 = x^2 + x^2$<br />$256 = 2x^2$<br />$x^2 = 128$<br />$x = \sqrt{128}$<br />$x = 8\sqrt{2}$<br /><br />Step 4: Now, we can use the Pythagorean theorem again to find the length of $\overline{GJ}$:<br />$GJ^2 = GH^2 - HJ^2$<br />$GJ^2 = (8\sqrt{2})^2 - (8)^2$<br />$GJ^2 = 128 - 64$<br />$GJ^2 = 64$<br />$GJ = \sqrt{64}$<br />$GJ = 8$<br /><br />Therefore, the length of $\overline{GJ}$ is 8 units.