Finding the slant height of the cone.

[Lexadis]

It's be greatly appreciated if the step guide to the answer is demonstrated.
Q: The ratio of the slant height and perpendicular height of a cone is 5:4. The diameter of the base is 12cm. Find the slant height of the cone.

I have tried using pythagoras relationship but I just can't figure out how by making use the ratio we're going to get the slant height.

Thank you for all help c:

 

[pappus]

It's be greatly appreciated if the step guide to the answer is demonstrated.
Q: The ratio of the slant height and perpendicular height of a cone is 5:4. The diameter of the base is 12cm. Find the slant height of the cone.

I have tried using pythagoras relationship but I just can't figure out how by making use the ratio we're going to get the slant height.

Thank you for all help c:

Draw a sketch of the perpendicular cross-section of the cone.

Let \(\displaystyle \displaystyle{h_s}\) denote the slant height and \(\displaystyle \displaystyle{h_p}\) the perpendicular height. Then you know:

\(\displaystyle \displaystyle{\frac{h_s}{h_p} = \frac54}\)

Solve for \(\displaystyle \displaystyle{h_s}\).

You know the length of the radius of the base circle.

Now use the Pythagorian theorem. Your equation contains \(\displaystyle \displaystyle{h_p}\) as the only variable. Solve for \(\displaystyle \displaystyle{h_p}\)

 

[Bob Brown MSEE]

I have tried using pythagoras :

slant : perpendicular = 5:4 =s : p

Is the same as saying
1) s/p = 5/4
You tried pythagoras
2) s^2 = (6cm)^2 + p^2

Now you have 2 equations and 2 unknowns (s and p).
Solve equations 1) and 2) for s.

 

[Lexadis]

Draw a sketch of the perpendicular cross-section of the cone.

Let \(\displaystyle \displaystyle{h_s}\) denote the slant height and \(\displaystyle \displaystyle{h_p}\) the perpendicular height. Then you know:

\(\displaystyle \displaystyle{\frac{h_s}{h_p} = \frac54}\)

Solve for \(\displaystyle \displaystyle{h_s}\).

You know the length of the radius of the base circle.

Now use the Pythagorian theorem. Your equation contains \(\displaystyle \displaystyle{h_p}\) as the only variable. Solve for \(\displaystyle \displaystyle{h_p}\)

Thank you Finally got it. Thank you very much again for your kind help c: