Question

In the right-angled $△$ LMN, $\angle$ M = ${90}^{\circ }.$ If l(LM) = 12 cm and l(LN) = 20 cm, find the length of seg MN

Answer 1

In the right angled triangle LMN, $\angle$ M = 90${}^{\circ }.$ Hence, side LN is the hypotenuse.

According to Pythagoras' theorem,

$(LN{)}^2=(MN{)}^2+(LM{)}^2$

$\Rightarrow (20{)}^2=(MN{)}^2+(12{)}^2$

$\Rightarrow 400=(MN{)}^2+144$

$\Rightarrow (MN{)}^2=400-144$

$\Rightarrow (MN{)}^2=256$

$\Rightarrow (MN{)}^2=(16{)}^2$

$\Rightarrow \left(MN\right)=16$

$\therefore$ Length of seg MN = 16 cm.