Question

What is the value of k ?

Answer 1

Answer: The value of k is 2.

Explanation:

From the figure it is noticed that the triangle LMN, LON and MNO are right angle triangle.

According to the pythagoras theorem,

$(hypotenuse)^2=(base)^2+(perpendicular)^2$

Use pythagoras theorem in triangle LON.

$(LN)^2=(ON)^2+(LO)^2$

$m^2=(4)^2+(8)^2$

$m^2=80$

Use pythagoras theorem in triangle MON.

$(MN)^2=(MO)^2+(NO)^2$

$l^2=k^2+(4)^2$

$l^2=k^2+16$        ...... (1)

Use pythagoras theorem in triangle LMN.

$(LM)^2=(MN)^2+(LN)^2$

$(8+k)^2=l^2+m^2$

$(8+k)^2=l^2+80$  

$(8+k)^2-80=l^2$    .... (2)

From equation (1) and (2), we get

$k^2+16=(8+k)^2-80$

$k^2+16=k^2+16k+64-80$

$16=16k-16$

$32=16k$

$k=2$

Therefore the value of k is 2.

Answer 2

I hope you can see my answer and how I arrived at it in the attached picture.

My answer is k = 2