Question

KN is the altitude to the hypotenuse ML. What is the length of KM? Beyond lost tbh..
A. 1 1/8
B. 5
C. 11
D. 21 1/3

Answer 1

using pythagorus theorem in triangle MKN,
y2=x2+82............(i)
also, using pythagorean theorem in triangle MNL,
y2+b2=(x+3)2
y2+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 2

y2−x2=64
from (ii)
x2+9+6x=y2+73
y2−x2=9+6x−73
now equating the values of
y2−x2
so 9+6x-73=64 6x-64=64 6x=128 x=21.33

Answer 3

or you can set up the proportion 3/8 = 8/x and solve for x

3/8 = 8/x

3x = 8*8

3x = 64

x = 64/3

x = 21.33333...

This proportion is valid because we have 3 similar triangles

Answer 4

Also, \[\Large \frac{64}{3} = 21 \frac{1}{3}\]

Answer 5

Thank you both. I really appreciate you all explaining the reason as to why it was. That honestly helped me.