Question

3) The diagonal of a square is 10 cm. then find the length of
its side and perimeter.​

Answer 1

Answer:

Diagonal of square =10cm

Also, diagonal of square =

2

×side

or,

2

×side=10⇒side=

2

10

=

2

10

2

=5

2

cm

∴ Area of square =(side)

2

=(5

2

)

2

=50cm

2

Answer 2

Answer:

In a square, a right angled triangle is formed by one of square's diagonal and two sides.

Also all sides of square are equal length.

Therefore, in ∆ABC by Pythagoras theorem , we have ; AC² = AB² + BC²

10² = AB² + AB². (Since AB = BC)

100 = 2AB²

50 = AB²

AB = √50

AB = √2×5×5

AB = 5√2cm

So, all sides of square are of 5√2cm.

Now perimeter of square = 4×side

= 4×5√2

= 20√2 cm. ANS.

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