Question

in triangle LMN L= 5 ,M= 13 , n= 12 state triangle LMN is a right angle triangle or not ​

Answer 1

Given : A ∆LMN, in which, LM = 5 units , MN = 13 units , NL = 12 units

To Find : Whether it is a right angled triangle or not.

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀____________________

$\: \:$

❍ In a right angled triangle, Sum of the squares of perpendicular and base is equal to the hypotenuse.

$\: \:$

$\star \: \underline{\boxed{\sf\pink{(Perpendicular {})^{2} + {(Base)}^{2} = {(Hypotenuse)}^{2} }}}$

$\: \:$

Here

$\: \:$

• Perpendicular = 12 units
• Base = 5 units
• Hypotenuse = 13 units

$\: \:$

Put the values in the formula and solve.

$\:$

$\sf:\implies \:P {}^{2} + B {}^{2} = H {}^{2} \\ \\ \\ \sf:\implies \: (12) {}^{2} + (5) {}^{2} = (13) {}^{2} \\ \\ \\ \sf:\implies \: 144 + 25 = 169 \\ \\ \\ \sf:\implies \:\underline{\boxed{\mathfrak\pink{169 = 169}}} \: \bigstar$

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀____________________

$\: \:$

$\:$

$\sf\therefore{\underline{Hence, \: triangle \: \bold{LMN} \: is \: a \:right \: angled \:triangle.}}$