Question

find the value of side x​

Answer 1

Hello!

Please refer to the modified diagrams below before starting to solve the above problem.

Look the simplified diagram,Fig.1, the red line here is the diagonal of square.

Modifying the diagram again using some results of square, we find out in Fig.2 the right angled triangle with perpendicular (14+9) cm = 23 cm and base 7 cm.

Now, Using pythagoaras theorem, we find the value of H which is the diagonal of square.

$H = \sqrt{P^2 + B^2}\\\\H = \sqrt{(23)^2 + 7^2}\\\\H =\sqrt{529 + 49}\\\\H = \sqrt{578}\\\\H = 17\sqrt2 \ cm$

The diagonal of square = $x\sqrt2$ by formula.

$17\sqrt2 = x\sqrt2\\\\or, \boxed{x = 17 \ cm}$

Hence, Length of square is 17 cm.

Answer 2

Given :  A Square of Side x    and few lines inside

To find : side of Square

Solution:

in Addition to Durgesh Pal Solution :

Another Way to Solve :

Let draw diagonal (x√2)  intersecting 7 cm side

hence getting y & 7 - y sides

We get two triangles

with sides 9 , y  & hypotenuse  = √(9² + y²)

& 14 & 7 - y   & hypotenuse  = √(14² + (7-y)²)

Both triangle will be similar as one angle is 90 deg in both triangles and one angle is vertically opposite ( hence equal)

=> y/7-y  = 9/14

=> 14y = 63 - 9y

=> 23y = 63

=>y = 63/23

Diagonal  =    √(9² + y²)  +  √(14² + (7-y)²)

=> x√2   =   √(9² + (63/23)²)  +  √(14² + (7-(63/23))²)

=> x√2   =   √(9² + (63/23)²)  +  √(14² + (98/23))²)

=> x√2   =  153√2 / 23    +   238√2 / 23

=> x = (153 + 238)/23

=> x = 391/23

=> x = 17

Side of Square = 17 cm

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