Question

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 =

Answer 1

Answer: 2

Step-by-step explanation:

Answer 2

Answer:

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,

$(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}$

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

$64 + 16k+k^{2} = 80+ 16 +k^{2} \\\\16k=96\\\\\therefore k=\frac{96}{16} \\\\\therefore k=6$

Therefore the value of k = 6.