Question

i got part A right and thought i had Part B with 22.8 but it tells me that is not correct. Im confused.

Answer 1

Consider the triangle shown below

This question will be solved using Pythagorean Theorem

Considering traingle KLN it follows:

`x^2=y^2+20^2`

Considering triangle LMN it follows:

`x^2=26^2-z^2`

Equate the x² values

`y^2+20^2=26^2-z^2`

Considering triangle KLM

`z^2=y^2^{}+6^2`

Substitute the value of z² into the previous equation

`y^2+20^2=26^2_{}-(y^2+6^2)`

Simplify the equation

`\begin{gathered} y^2+20^2=26^2_{}-y^2-6^2 \\ y^2+y^2=26^2-6^2-20^2 \\ 2y^2=240 \\ y^2=120 \end{gathered}`

Substitute y² into x²=y²+20²

`\begin{gathered} x^2=120+20^2 \\ x^2=120+400 \\ x^2=520 \\ x=\sqrt[]{520}^{} \\ x=2\sqrt[]{130} \end{gathered}`

Therefore the value of LN is

`2\sqrt[]{130}`