Question

Please help with geometric mean!!

Answer 1

The exact value of y is $4\sqrt{3}$.

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.

$h^2=pq$

$h^2=2\times6$

$h^2=12$

Taking square root on both sides,

$h=\sqrt{12}$

Using Pythagoras theorem,

In right triangle, square of the hypotenuse is equal to the sum of the squares of the other two sides.

$y^2=(\sqrt{12})^2+6^2$

$y^2=12+36$

$y^2=48$

$y=4\sqrt{3}$

The exact value of y is $4\sqrt{3}$.