Question

Please help with geometric mean!!

Answer 1

The exact value of y is
`4√(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*6`

`h^2=12`

Taking square root on both sides,

`h=√(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=(√(12))^2+6^2`

`y^2=12+36`

`y^2=48`

`y=4√(3)`

The exact value of y is
`4√(3)`.