The exact value of y is [tex]4\sqrt{3}[/tex].
Solution:
The attached below shows how the formula is written.
Using geometric mean,
Total base length (p + q) = 8
q = 6
p = 8 – 6 = 2
Let us first find the height of the triangle.
[tex]h^2=pq[/tex]
[tex]h^2=2\times6[/tex]
[tex]h^2=12[/tex]
Taking square root on both sides,
[tex]h=\sqrt{12}[/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]y^2=(\sqrt{12})^2+6^2[/tex]
[tex]y^2=12+36[/tex]
[tex]y^2=48[/tex]
[tex]y=4\sqrt{3}[/tex]
The exact value of y is [tex]4\sqrt{3}[/tex].
