What is the area of a square with the dimension of 1+√3?

Question

~I have this tricky, multiple-choice question on a really important exam that I have to take for Algebra 1... I know how to do the problem (stated in the question above), but somehow the answers are all different from my result... I mean, if the dimension of a square is 1+√3, all I have to do is FOIL, right? (1+√3)(1+√3) The only problem is, I must be doing something wrong... The answers on the exam say:

a). 4
b). 4 + 2√2
c). 3√3
d). 5

Could somebody please explain this to me, pretty please? :-)

Thanks a ton!!

~Juby~

Answer 1

The book must simply be in error. By dimension, they must mean the edge of the square is 1 + √3 units long. Squaring that, one gets:

(1 + √3)(1 + √3) = 1 + 2√3 + 3 = 4 + 2√3 units.

The choice closest to that seems to be b. So, they probably have a misprint in the book.

Answer 2

If 1 + sqrt(3) is the side of the square, its area is:
(1 + sqrt(3))^2
= 1^2 + 3 + 2sqrt(3)
= 4 + 2sqrt(3).

There is no way you could get 4 + 2sqrt(2). That must be a misprint. You were right.

Answer 3

You're method seems to be correct, for the way the question is stated. I get a value of 4 + 2sqrt(3), which i'm sure is what you came up with. My guess is that answere b) is a misprint. If I were you, I would talk to you teacher about it, sometimes they make mistakes :)

Answer 4

Sounds like a typo on the part of the instructor. The correct answer is of course 4 + 2SQRT(3). Teachers are human too and sometimes make mistakes.