Question

Given rectangle PQRS with PQ=QR, PQ=SP, and SQ=6√2. Find SR. a)√2. b) 6. c) 5√2 d) not enough information

Answer 1

The rectangle is actually a square. In fact, we have that the side PQ is equal to 2 other sides of the rectangle (QR and SP), and this is possible only if all the 4 sides of the rectangle are equal: this means it is a square.

SQ is the diagonal of the square:
`SQ = 6 √(2)`, but we know that in a square, the diagonal is equal to square root of 2 times the length of the side:

`d = √(2) L`
where d is the diagonal and L the length of the side. Since in our square the length of the diagonal is
`d= 6 √(2)`, the length of the side must be

`L= (d)/( √(2) ) = (6 √(2) )/( √(2) )=6`

so, the correct answer is b) 6.