Answer:
[tex]x=12\sqrt{6}\ units\\ \\y=12\sqrt{2}\ units[/tex]
Step-by-step explanation:
In a right triangle, the height drawn to the hypotenuse is geometric mean between the measures of the two segments of the hypotenuse, so
[tex]y^2=24\cdot 12\\ \\y^2=2\cdot 12\cdot 12\\ \\y=\sqrt{2\cdot 12\cdot 12}\\ \\y=12\sqrt{2}\ units[/tex]
If the height is drawn to the hypotenuse in a right triangle, each leg of the right triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg. So
[tex]x^2=24\cdot (24+12)\\ \\x^2=24\cdot 36\\ \\x^2=4\cdot 6\cdot 36\\ \\x=\sqrt{4\cdot 6\cdot 36}\\ \\=x=2\cdot 6\sqrt{6}\\ \\x=12\sqrt{6}\ units[/tex]
