Question

find perimeter of a square if its diagonal is 10 into square root 2 what is the answer

Answer 1

Diagonal =10×root 2
Diagonal =14•14
Area=99•96
side×side=99•96
side=9.997
Perimeter=4×side
perimeter= 40 or39•988

Answer 2

Let the sides of the square are a unit each

We know that the adjacent sides of square are perpendicular to each other and equal in length.

As they are perpendicular, angle between two adjacent side is 90° .

By Pythagoras Theorem,

( side )^2 + ( side )^2 = ( hypotenuse )^2

If we distribute square in two right angles, we will get a hypotenuse which is the diagonal of the square.

∴ ( a )^2 + ( a )^2 = ( diagonal )^2

In the question value of length of the diagonal is 10√2 unit .

⇒ a^2 + a^2 = ( 10√2 )^2

⇒ 2a^2 = ( 100 x 2 )

⇒ a^2 = $\bold{\dfrac{100 \times 2 }{2} }$

⇒ a^2 = 10 unit^2

⇒ a = 10 unit

Therefore the length of the sides of the square is 10 unit.

We know, perimeter of the square = 4 x side

∴ Perimeter of this square = 4 x 10 units

⇒ Perimeter of this square = 40 units

Hence, perimeter of this square is 40 units.