Question

Please Solve the question​

Answer 1

Answer:

15

Step-by-step explanation:

A diagram is attached for better understanding.

 In that diagram :

     Length of the rectangle is 12 and breadth is 3( since three angles are of measure 90°, remaining too, must be of 90° by 360° - 90° - 90° - 90° ).

 Now, in ΔABC( right-angled triangle ) : longer side is 9 + 12 = 21 and shorter( other leg ) is 3.

On observation :

  Hypotenuse of ABC = diagonal of square

        By Pythagoras theorem:

    { diagonal of square is given by √( side^2 + side^2 ) and hypotenuse of a triangle is given by √( height^2 + base^2 ) }. Here, side is x and in that triangle height is 12 + 9 and base is 3.

⇒ √{ ( 12 + 9 )^2 + 3^2 } = √( x^2 + x^2 )

⇒ √{ 21^2 + 3^2 } = √( 2x^2 )

⇒ 441 + 9 = 2x^2

⇒ 450 = 2x^2

⇒ 450 / 2 = x^2

⇒ 225 = x^2

⇒ 15 = x

        Hence the required value of x is 15.

Answer 2

$\tt{\orange {\huge{ Hello!!! }}}$

QUESTION :

See the attachment in the question.

Please Solve the question...

SOLUTION :

Let the side of the square be X cm.

Join the diagonal of the square.

Now :

$\sqrt{ ( 12 + 9 )^2 + 3^2 } = \sqrt { x^2 + x^2 } \\ \\</p><p></p><p>\sqrt { {21}^2 + {3}^2 } = \sqrt{ {2x}^2 } \\ \\</p><p></p><p>Squaring \: Both \: Sides$

$4{x}^2 = 450 \\ \\ {x}^2 =225 \\ \\ x = 15$

So the length of the square is 15 cm......(A)