Question

KN is the altitude to the hypotenuse ML. What is the length of KM?
http://secure.starssuite.com/files/geo2010/Geom_10S_Fig26.jpg

Answer 1

Using pythagorus theorem in triangle NKL,
\[8^{2}+3^{2}=b ^{2}\]
\[b=\sqrt{73}\]

Answer 2

using pythagorus theorem in triangle MKN,
\[y ^{2}=x ^{2}+8^{2}............(i)\]
also, using pythagorean theorem in triangle MNL,
\[y ^{2}+b ^{2}=(x+3)^{2}\]
\[y ^{2}+73=(x+3)^{2}..............(ii)\]
so , now we have left with two equations in 2 variables,
solve them using any method to find x and y.
and x is the required value i.e.,x=MK

Answer 3

from (i)
\[y ^{2}-x ^{2}=64\]
from (ii)
\[x ^{2}+9+6x=y ^{2}+73\]
\[y ^{2}-x ^{2}=9+6x-73\]
now equating the values of \[y ^{2}-x ^{2}\]
so
9+6x-73=64
6x-64=64
6x=128
x=21.33

Answer 4

thank you!!!!

Answer 5

you're welcome......:)