The length of AB = 8 units.
Solution:
The attached below shows how the formula is written.
Using geometric mean,
p = 4 units and q = 12 units
Let us first find the height of the triangle.
[tex]h^2=pq[/tex]
[tex]h^2=4\times12[/tex]
[tex]h^2=48[/tex]
Taking square root on both sides,
[tex]h=\sqrt{48}[/tex]
Using Pythagoras theorem,
In right triangle, square of the hypotenuse is equal to the sum of the squares of the other two sides.
[tex]AB^2=(\sqrt{48})^2+4^2[/tex]
[tex]AB^2=48+16[/tex]
[tex]AB^2=64[/tex]
Taking square root on both sides.
AB = 8 units
The length of AB = 8 units.
