Question

I will give brainliest if you answer please

Answer 1

Answer:

KN = 11

Step-by-step explanation:

In right triangle LNM, by Pythagoras theorem:

$LN=\sqrt{LM^2 -MN^2} \\ \\ \implies \: LN=\sqrt{ {(100)}^{2} -(80)^2} \\ \\ \implies \: LN=\sqrt{ 10000 -6400} \\ \\ \implies \: LN=\sqrt{ 3600} \\ \\ \implies \: LN=60$

In right triangle LNK, by Pythagoras theorem:

$KN = \sqrt{LK^2-LN^2}$

$\implies KN = \sqrt{(61)^2-(60)^2}$

$\implies KN = \sqrt{3721-3600}$

$\implies KN = \sqrt{121}$

$\implies\huge{\orange{ KN =11}}$

Answer 2

Answer:

• 11

$\:$

Step-by-step explanation:

Before, Finding the length of KN, we must have to find the length of LN. So

$\:$

Here, LNM is a right angled triangle where measure of two sides are given and we are to find the measure of the third side LN(Perpendicular).

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We'll find the measure of third side with the help of the Pythagorean theorem.

$\\ {\longrightarrow \pmb{\sf {\qquad (Base) {}^{2} + (Perpendicular {)}^{2} = (Hypotenuse {)}^{2} }}}$

Here,

• The base (NM) is 80

• The perpendicular is LN

• The hypotenuse (LM) is 100.

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So, substituting the values in the above formula we get :

$\\ {\longrightarrow \pmb{\sf {\qquad (NM) {}^{2} + (LN {)}^{2} = ( LM{)}^{2} }}}$

${\longrightarrow \pmb{\sf {\qquad (80) {}^{2} + (LN {)}^{2} = ( 100{)}^{2} }}}$

${\longrightarrow \pmb{\sf {\qquad (LN {)}^{2} = ( 100{)}^{2} - (80) {}^{2}}}}$

${\longrightarrow \pmb{\sf {\qquad (LN {)}^{2} = 10000 - 6400}}}$

${\longrightarrow \pmb{\sf {\qquad (LN {)}^{2} = 3600}}}$

${\longrightarrow \pmb{\sf {\qquad LN = \sqrt{3600} }}}$

${\longrightarrow \pmb{\sf {\qquad LN = \frak{60}}}}$

Therefore,

• The length of LN is 60.

As, we found the length of LN, now we can find the length of KN.

Where,

• The base is KN

• The perpendicular (LN) is 60.

• The hypotenuse (LK) is 61.

So, in the right angled triangle LKN, by Pythagorean theorem we get,

$\\ {\longrightarrow \pmb{\sf {\qquad (KN) {}^{2} + (LN {)}^{2} = ( LK{)}^{2} }}}$

${\longrightarrow \pmb{\sf {\qquad (KN) {}^{2} + {60}^{2} = ( 61{)}^{2} }}}$

${\longrightarrow \pmb{\sf {\qquad (KN) {}^{2} = ( 61{)}^{2} - {(60)}^{2}}}}$

${\longrightarrow \pmb{\sf {\qquad (KN) {}^{2} =3721 - 3600}}}$

${\longrightarrow \pmb{\sf {\qquad (KN) {}^{2} = 121}}}$

${\longrightarrow \pmb{\sf {\qquad KN = \sqrt{121} }}}$

${\longrightarrow \pmb{\sf {\qquad KN = \frak{11} }}}$

Therefore,

• The length of KN is 11.