Question

I need help!! This is getting a little harder than I expected

Answer 1

Length of the side = 9 cm

Diagonal = $9\sqrt{2}$ cm

Solution:

Area of the square = 81 square centimeters

In square all sides are equal.

Area of the square = side × side

Side × side = 81

Side² = 9²    (∵81 = 9²)

Taking square root on both sides, we get

Side = 9 cm

Length of the side = 9 cm

To find the length of the diagonal:

In square all the angles are right angle.

Diagonal splits the square into two right angle triangle.

Using Pythagoras theorem,

In right triangle, square of the hypotenuse is equal to the sum of the square of the other two sides.

Here, diagonal is the hypotenuse.

$\text{Diagonal}^2=9^2+9^2$

$\text{Diagonal}^2=81+81$

$\text{Diagonal}^2=2\times 81$

Taking square root on both side,

Diagonal = $9\sqrt{2}$ cm