Question

the length of the diagonal of a square is 20 cm.what is its area

Answer 1

Here is your solutions

Given :-

The length of the diagonal of a square is 20cm (diagonal = hypotenuse )

Let side of square be x

in square there is two triangle.

in right angle triangle
H^2 = p^2 + b^2

$d {}^{2} \: = x {}^{2} + x {}^{2} \\ 20 {}^{2} = 2x {}^{2} \\10 {}^{2} = x {}^{2}\\ 100 = x {}^{2} \\ 10 = x$
Hence

Area of square = side × side

=>10 ×10 = 100cm^2

Hope it helps you

Answer 2

Here's the answer!

In the adjoining figure,

$\bf {\square ABCD \: is \: a \: square}$
Thus,
As each angle of square is right angled,

Angle ABC = 90°

Thus,
By Pythagoras theorem,

$\bf{AB {}^{2} + BC {}^{2} = AC {}^{2} }$

Now,

Each side of a square are equal.
So let each side be 'x'.

Thus,

$\bf{x {}^{2} + x {}^{2} = 20{}^{2}}$

$\bf{2x {}^{2} = {20}^2}$

$\bf{x {}^{2} = \frac{{20}^2}{2} }$

$\bf {{x}^{2} = {10}^2}$

$\bf{ x = 10 }$

Side of the square is 10 cm.

Now,

Area of square = Side × Side

= 10 × 10

= 100 sq. cm.

Area of square is 100 sq.cm