Question

Find the perimeter of a square whose diagonal is 5√2 cm

Answer 1

Given,

The diagonal of the square is 5√2 cm.

To Find,

The perimeter of the square.

Solution,

To calculate the area of the square, we need the length of a side of the square.

Let the side of the square be x cm.

By using the Pythagoras theorem,

x²+x² = (5√2)²

2x² = 25*2

x² = 25

x = 5cm.

Now, the perimeter of square = 4*side

Perimeter = 4*5 = 20 cm

Hence, the perimeter of the square is 20 cm.

Answer 2

square, in geometry, a plane figure with four equal sides and four right (90°) angles. A square is a special kind of rectangle (an equilateral one) and a special kind of parallelogram (an equilateral and equiangular one).

Diagonal of a square is $5\sqrt{2}cm$

Find the perimeter of square.

According to the question,

Let the side of square be $x$

Apply Pythagoras theorem

$x^2+x^2=(5\sqrt{2})^2$

$2x^2=25\times 2$

$x^2=25$

$x=5$

So, the side of square is $5cm$.

perimeter of square is $=4\times side$

$=4\times 5$

$=20cm$