Question

14. A right-angled triangle LMN is shown below.

Answer 1

Answer:

The Length of MN is 15.6 cm.

Step-by-step explanation:

Given:

A right angled triangle LMN at angle M is equal to 90°

LN = Hypotenuse = 16.9 cm

LM = Shorter leg  = 6.5 cm

To Find:

MN = Longer leg = ?

Solution:

In Right Angled Triangle Δ LMN

Pythagoras Theorem States that

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

By applying Pythagoras theorem we get

$l(LN)^{2}= l(LM)^{2}+l(MN)^{2} \\\textrm{substituting the given values of we get}\\\\16.9^{2}= 6.5^{2}+ (MN)^{2}\\ \therefore (MN)^{2}=285.61-42.25\\l(MN)^{2}=243.36\\l(MN)=\pm \sqrt{243.36}\\l(MN)=15.6\ cm .........\textrm{as distance cannot be in negative}$

The Length of MN is 15.6 cm.