If l and w represent the length and width, respectively, of the rectan

i spent more time on thinking whether B is a trap or not, since 10 is 2x5, and we know the pythagorean triplet 3-4-5 multiplied by 2 or 6-8-10.
even the first statement might suggest that l=8 and w=6 since 6*8 = 48
but!!!
if you do the math, you see that lw = 48, and l^2 + w^2 = 100
knowing that (a+b)^2 = a^2+2ab+b^2, we can easily see that l^2+2lw+w^2 = 196 or (l+w)^2 = 196
l+w will thus be 14 and the perimeter 32. we can get to the correct answer only by combining the two statements.
C is the answer.

Rephrasing the question: "what is the perimeter of the rectangle?" i.e. \(2*(l+w) = ?\)

(1) The area of the rectangle is 48
Mathematically, this means that \(l*w = 48\). This piece of information is not sufficient by itself.
Hence, the statement is insufficient (eliminate A and D).

(2) The length of a diagonal of the rectangle is 10
Since rectangles have right angles in their corners, the diagonal of any rectangle can be obtained through Pythagoras' theorem. Mathematically, this means that \(\sqrt{l^2+w^2} = 10\). This piece of information is not sufficient by itself.
Hence, the statement is insufficient (eliminate B).

(1) + (2) The area of the rectangle is 48 and the length of a diagonal of the rectangle is 10
This statement gives us two mathematical formulas:
\(l*w = 48\)
\(\sqrt{l^2+w^2} = 10\)
If one recalls, one of the basic mathematical identities is \((a+b)^2 = a^2 + 2*ab + b^2\). Hence, if we plug the two formulas above into the latter identity, we get:
\((l+w)^2 = l^2 + w^2 + 2*l*w = 10^2 + 2*48 = 196 = 14^2\)
Thus, \(2*(l+w) = 2*14 = 28\).
This is sufficient to answer the question.

Answer: C