Question

If the diagonal of a
square is 25√2cm then the length
of its side is-----
options:50cm,25cm ,5cm,5√2cm​

Answer 1

Answer:

25

Step-by-step explanation:

diagnol of square =a√2 where a is side of a square

so a√2=25√2

a=25

Answer 2

Answer:

The length of side of square is 25 cm.

Option ( B ) 25 cm.

Step-by-step-explanation:

NOTE: Refer to the attachment for the diagram.

In figure, ☐ABCD is a square.

∴ AB = BC = CD = AD - - [ Sides of a square ] ( 1 )

And AC is diagnonal.

$\sf\:AC\:=\:25\:\sqrt{2}\:cm\\\\\\\sf\:Now,\:\:In\:\triangle\:ABC\:,\:\measureangle\:ABC\:=\:90^{\circ}\:\:\:-\:-\:[\:Angle\:of\:a\:square\:]\\\\\\\therefore\sf\:AC^2\:=\:AB^2\:+\:BC^2\:\:\:-\:-\:[\:Pythagoras\:theorem\:]\\\\\\\implies\sf\:(\:25\:\sqrt{2}\:)^2\:=\:AB^2\:+\:AB^2\:\:\:-\:-\:[\:From\:(\:1\:)\:]\\\\\\\implies\sf\:(\:25\:)^2\:\times\:2\:=\:2\:AB^2\\\\\\\implies\sf\:625\:\times\:\cancel{2}\:=\:\cancel{2}\:\times\:AB^2\\\\\\\implies\sf\:AB^2\:=\:625\\\\\\\implies\sf\:AB\:=\:\sqrt{625}\:\:\:-\:-\:[\:Taking\:square\:roots\:]\\\\\\\implies\sf\:AB\:=\:\sqrt{25\:\times\:25}\\\\\\\implies\boxed{\red{\sf\:AB\:=\:25\:cm}}\\\\\\\underline{\sf\:The\:length\:of\:side\:of\:square\:is\:25\:cm}}$

$\bigstar\:\boxed{\sf\:Alternative\:method}\\\\\\\pink{\sf\:Diagonal\:of\:Square\:=\:side\:\sqrt{2}}\\\\\\\implies\sf\:25\:\cancel{\sqrt{2}}\:=\:side\:\cancel{\sqrt{2}}\\\\\\\therefore\underline{\sf\:Side\:of\:square\:=\:25\:cm}$