What is the area of rectangle ABCD?

Hi,

Question:
What is the area of rectangle ABCD?

i.e., Area of rectangle = l * w

We need to find the values of l *w or any relation which gives l*w

Statement I is insufficient:

l^2 + 2lw + w^2 = 16

Immediately we can think of (a+b)^2 = a^2 + b^2 + 2ab.

(l+w)^2 = 16.

Taking square root on both sides(side length and area can’t be negative).

l+w = 4

But “l” and “w” can take different values.

l = w = 2. Then the area would be 4.

Or

l = 1 and w = 3. Then the area would be 3.

So insufficient.

Statement II is insufficient:

l^2 – 2lw + w^2 = 4

similar to statement I, it is (a-b)^2 = a^2 + b^2 - 2ab

(l-w)^2 = 4.

Taking square root on both sides(side length and area can’t be negative).

l-w = 2

But “l” and “w” can take different values.

l =4 and w = 2. Then the area would be 8.

Or

l = 3 and w = 1. Then the area would be 3.

We can come up with different values of l and w. So area keep changing.

So insufficient.

Together it is sufficient.

l – w = 2

and l + w = 4

Solving we get l = 3 and w = 1

So, the area of the rectangle has to be 3.

So the answer is C (together sufficient).