Between which two integers does square root of 12 lie?

a.
3 and 4

b.
5 and 7

c.
11 and 13

d.
143 and 145

A. 3 and 4

We know the square root of 9 is 3, and the square root of 16 is 4, so the square root of 12, which is between 9 and 16, must be between 3 and 4.

A rectangle is a quadrilateral with either two opposite sides equal and parallel to each other. That is AB is parallel and equal to CD and AD parallel and equal to BC. Parallel lines have equal slopes.
Thus, AB slope is 2, while that of CD is also 2, therefore they are parallel to each other. In addition the modulus of AB and that of CD is the same thus they are equal in length.
AD slope is -1/2 while that of BC is also -1/2 therefore the two are parallel to each other. In addition they are equal in length therefore they are equal in length. 
Moreover AB is perpendicular to BC and AD (product of slope of two perpendicular lines is -1)
Therefore, it can be concluded that Quadrilateral ABCD is a rectangle.