What is the area of the rectangular region above?
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04 Nov 2021, 03:34
Here is how i would solve this problem:
We are interested in the area of this rectangular region, which is L x W= ?
Statement 1/
L+W= 6 is clearly not sufficient!
If L= 5 and W= 1 , then the area would be 5 x 1= 5, on the other side
if L=4 and W=2, then the area would be 4 x 2= 8,
Thus, since we get different values for the area of this rectangular region, statement 1 is clearly Not Sufficient!
Statement 2/
D^2=20 is clearly not sufficient. The diagonal of a rectangle can be found using Pythagorean Theorem, but we need atleast 2 sides to find the third one and since statement 2 gives us just one side, hence Not sufficient.
Statement 1 and 2 together, are sufficient and here is why:
From statement 1: for L+W=6, we had two scenarios: 5+1=6 or 4+2=6.
From statement 2: D^2=20.
So if we apply the Pythagorean Theorem for the diagonal of the rectangle, which is D, then we come to the conclusion that from the 2 different scenarios we had from statement 1, inwhich L+W=6, just one of them fits the Pythagorean Theorem for the diagonal of the rectangle, and that is when L=4 and W=2, which gives L+W=6.
Pythagorean Theorem:
a^2+b^2=c^2 (C stands for the diagonal, which is D according statement 2), and lets check if that is the case.
4^2 + 2^2 = D^2
16+4=20, thus gives 20 for D^2.
Thus, the area L * W=4 * 2= 8
Both statements together are Sufficient! C