[SpaceBar]

W=WIDTH, L=LENGTH

---

L*W = 12
and
2(L + W) = x (where x is one of the four possible values)
solve first eq for W...
W = 12/L
substitute in second giving
2L + 24/L = x
divide by 2...
L + 12/L = x/2
multiply both sides by L and rearrange...
L^2 - (x/2)L + 12 = 0
substituting each value (12,14,15,21) into this eq yields a quadratic that can be solved.
Answer “A” has no real roots, but B,C, and D all have nondegenerate real roots, therefore B,C or D are valid answers, but not A.

[SpaceBar]

nondegenerate positive real roots

[The Truth Will Make You Free]

Yes. B, C, and D could all be correct. Any answer over two times the square root of 12 could be correct. For example, 96.5 would be correct if the blanket were 48 units long and 0.25 units wide. The only answer among those given where the sides are whole numbers is 14.

[TontoKowalski]

L*W = 12 and 2(L + W) = x (where x is one of the four possible values) solve first eq for W... W = 12/L substitute in second giving 2L + 24/L = x divide by 2... L + 12/L = x/2 multiply both sides by L and rearrange... L^2 - (x/2)L + 12 = 0 substituting each value (12,14,15,21) into this eq yields a quadratic that can be solved. Answer “A” has no real roots, but B,C, and D all have nondegenerate real roots, therefore B,C or D are valid answers, but not A.

I approached the problem from a "system of equations" perspective, and I agree with your analysis. My solution is that there are "infinite solutions" but that one of them is not A.

But then I realized that the problem does not specify that the blanket is rectangular, so we have to assume this in order to use our approach.

I am also frankly shocked that so many wise freepers just assume that the blanket sides must be in neat and tidy integer unit lengths, even if one concedes that the blanket must be rectangular. Nothing in the problem precludes a rectangle with a length 4.5 units, for example.

However, I believe we can safely say that the student is "supposed" to imagine a 3x4 rectangular blanket, provided the student is in a public grade school.

This thread is a candidate for the Hall of Fame. It embodies so many qualities that make Freeping a fun and unique experience.