Question

If diagonal of square is 12root2 cm then find side of the square​

Answer 1

Step-by-step explanation:

x^2+x^2=12√2^2

2x^2 =144×2

2x^2=288

x^2=144

x=12

Answer 2

Solution

First let us draw the square ABCD

Refer to attachment

Diagonal of the square AC = 12√2 cm

Let the length of the side of the square ( AB, AC ) be 's' cm

Consider the ΔABC

∠ABC = 90° [ Angle in a square ]

Therefore, ΔABC is a Right angled triangle

By pythagoras theorem

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

Substituting the values

$\implies s^{2} + s^{2} = (12 \sqrt{2} )^{2}$

$\implies 2s^{2} = {12}^{2} \times 2$

$\implies s^{2} = \dfrac{ {12}^{2} \times 2}{2}$

$\implies s^{2} = {12}^{2}$

$\implies \boxed{s = {12}}$

Hence, the length of the side of the square is 12 cm.