Question

If the end points of a diagonal of a square are 1 -2 3 & 2-3 5 then find the length of the side of square

Answer 1

Answer:

√3 units

Step-by-step explanation:

Given that,

The end points of a diagonal of a square are :

• (1,-2,3)
• (2,-3,5)

To find the length of the sides.

First of all, lets find the length of diagonal.

Let, the diagonal be d.

Therefore, we will get,

$= > d = \sqrt{ {(1 - 2)}^{2} + {( - 2 + 3)}^{2} + {(3 - 5)}^{2} } \\ \\ = > d = \sqrt{ {( - 1)}^{2} + {(1)}^{2} + {( - 2)}^{2} } \\ \\ = > d = \sqrt{1 + 1 + 4} \\ \\ = > d = \sqrt{6}$

Therefore, length of diagonal is √6 units.

Now, let the length of each side be a.

But, we know that,

• d = √2a

Therefore, we will get,

=> √2a = √6

=> a = √6/√2

=> a = √3

Hence, required length of sides is √3 units.

Answer 2

Answer:

√3 units

Step-by-step explanation:

Given that,

The end points of a diagonal of a square are :

(1,-2,3)

(2,-3,5)

To find the length of the sides.

First of all, lets find the length of diagonal.

Let, the diagonal be d.

Therefore, we will get,

Therefore, length of diagonal is √6 units.

Now, let the length of each side be a.

But, we know that,

d = √2a

Therefore, we will get,

=> √2a = √6

=> a = √6/√2

=> a = √3

Hence, required length of sides is √3 units.

Step-by-step explanation: