Triangle l n m is shown. angle l n m is a right angle. an altitude is drawn from point n to point o on side l m, forming a right angle. side l n is labeled m, side n m is labeled l, and line segment o m is labeled k. the length of n o is 4 and the length of l o is 8. what is the value of k? k =

Therefore the value of k = 6.

Step-by-step explanation:

Given:

LN = m

NM = l

OM = k

NO = 4

LO = 8

LM = 8 + k and

Δ LNM ,Δ LON and Δ MON are right Triangle.

To Find :

Om = k = ?

Solution:

In Right angle Triangle By Pythagoras Theorem we have,

So, In Right angle Triangle Δ LON we have,

LN² = ON² + OL²

m² = 4² + 8²

m² = 80   ............( 1 )

Now in  Right angle Triangle Δ MON we have,

MN² =  ON² + MO²

l² = 4² + k² ....................( 2 )

Now In Right angle Triangle Δ LNM we have,

LM² = LN² + MN²

(8 + k)² = m² + l² .................( 3 )

Substituting equation  1 and equation 2 in equation 3

(8+k)² = 80 + 4² + k²

Applying (A+B)² = A² +2AB + B² we get

Therefore the value of k = 6.

the line of

answer: 12

step-by-step explanation:

because yes