Question

A(3, 6) and B(4, 7) are two adjacent vertices of a square ABCD. Find the length of each side of the square.

Answer 1

length of side =
`√(2)`

Explanation:

the sides of a square are congruent

find the length of side AB using the distance formula

d =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`

with (x₁, y₁ ) = A (3, 6 ) and (x₂, y₂ ) = B (4, 7 )

d =
`√((4-3)^2+(7-6)^2)`

=
`√(1^2+1^2)`

=
`√(1+1)`

=
`√(2)`

Then the exact length of each side of the square is
`√(2)`