Question

What is the value of k ?

Answer 1

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

My answer is k = 2

Answer 2

Answer: The value of k is 2.

Step-by-step 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.