Welcome 2016! Part 29

Let the length and breadth of rectangle be $x , y$
Then,
$\large 2(x+y) = 14 \Rightarrow x+ y = 7$ $\large \text{Area of Square} = (x+y)^2 = 7^2 = \color{#3D99F6}{49}$

Let the sides of congruent rectangles be $\color{#3D99F6}{x,7-x}$ (since their sum is 7). Now if we carefully notice the side of bigger square, we observe that it is the sum of smaller side of one rectangle and bigger side of another congruent rectangle i.e (7-x)+x=7. Therefore area $\color{#D61F06}{=7^2=49}$

I'm sure you should put 25 as an answer choice instead of 28.

length of side of square=l+b=14/2=7. area of square = 7^2=49

the sum of smaller side and larger side of the rectangle is the side length of the square. that is, half its perimeter is the side length of square. hence side length of square is 14/2=7 so its area is 7*7=49

The length of square = l+b/2 The area of square= (l+b/2) (l+b/2) 7 7=49