Question

What is the perimeter of a square whose diagonal is 3 radical 2

Answer 1

a square is made up of 2 congruent right triangles with the same leg length. we use the Pythagorean theorem to find the length of one of these legs. a^2+b^2=c^2, but we know that the legs are equal in length, so we have 2a^2=(3rad2)^2

2a^2=9*2

a^2=9

a=3

square is made up of 4 of these, so 4*3=12

the perimeter is 12