Feeling dumb, can’t get to the end of this one. Can someone explain?
In a certain right triangle, the height is the average of the base and hypotenuse. If the area is kh2, where h is the height - then k is…?
Link: https://www.gregmat.com/problems/problem/in-a-certain-right-triangle-the-height-is-the-average/
Hi @jesshaw
Basically we need to establish two relationships before we can figure out what K is.
Now we have to use the Pythagoras theorem to make the 1st relationship simpler. i.e. find substitute expressions for Hypotenuse.
We know that, Hypotenuse^2 = Height^2 + Base^2 . You can solve this to get the following expression: Hypotenuse = (h^2 + b^2)^1/2 . This can be substituted in the 1st relationship to get : b = 3h/4.
Finally we can use substitution one last time in the 2nd relationship in order to find k.
So we replace the Base value as follows, (3h/4*h)/2 = kh^2
H^2 gets cancelled from LHS and RHS. Giving you k value as 3/8.
Hope this helps.
Jeet
my bad, didn’t see you already solved it ^^
Choosing numbers helps in this one. Hint: 3-4-5 triangle.
Thanks everyone!
