Question

The side legnth of a square is 11cm . Find the legnth of its diagonal correct to three decimal places.​

Answer 1

$\boxed{\red{ANS}{\blue{WER}}}$

$\overbrace{\underbrace{\large{Given\: :}}}$

$\longrightarrow{\textsf{The length of the side of a square is 11 cm }}$

$\bigstar{\Large{\textsf{Required to find\: :}}}$

$\bold{\textsf{1. Length of the diagonal ? }}$

✪ Condition Mentioned :

$\rightarrow{\textsf{1. Length of Diagonal upto 3 decimal places }{\leftarrow}}$

Condition Used ✏ :

$\implies{\fbox{\color{blue}{\longrightarrow{\boxed{(side{)}^{2} +(side{)}^{2} = (diagonal{)}^{2}}}}}}$

☞ Explanation :

➼ We can solve this question very simply.

➼ Just you should know that ;

➼ In a square a diagonal divides it into 2 congruent right angled triangles .

➼ Hence ,

➼The word right-angled triangle will actually state that we can use the pythagoran theorem here .

➼ So ;

➼ Actually the pythagoran theorem states that ;

$\boxed{\longrightarrow{\boxed{(side{)}^{2} +(side{)}^{2} = (hypotenuse{)}^{2}}}}$

➼ Hence ;

☆ Using the above condition;

➼ We can find the length of the diagonal .

➼ The condition in case of the square is instead of hypotenuse it is stated as diagonal.

So;

➼ The theorem condition will actually become

$\implies{\boxed{\longrightarrow{\boxed{(side{)}^{2} +(side{)}^{2} = (diagonal{)}^{2}}}}}$

➼ Hence, By substituting the respective values we can find the length of the diagonal .

Solution ✍ :

Side of the square = 11 cm .

Condition to be used ;

$\large{\boxed{\longrightarrow{\boxed{(side{)}^{2} +(side{)}^{2} = (diagonal{)}^{2}}}}}$

Hence ;

$\longrightarrow{{11}^{2} + {11}^{2} = {diagonal}^{2}}$

$\longrightarrow{ 121 + 121 = {diagonal}^{2}}$

$\longrightarrow{ 242 = {diagonal}^{2}}$

However;

$\longrightarrow{ {diagonal}^{2} = 242 }$

$\longrightarrow{ diagonal = \sqrt {242}}$

$\implies{\textsf{ diagonal = 15.556 (approximately)}}$

Therefore;

$\longrightarrow{\fbox{\color{red}{\Rightarrow{\textsf{ Diagonal = 15.556 cm }}}}}$

✅ Hence Solved.. ⇈