$ABCD$ is a square and $AEFG$ is a rectangle. Area of each of them is 36 sq. m. $E$ is the mid-point of $AB$. The perimeter of the rectangle $AEFG$ is

### Concept & Geometry When a point is described as a midpoint of a square's side, it perfectly bisects that side. We can use the square's area to find its full side, halve it to find one dimension of the rectangle, and use the rectangle's area to find its remaining dimension. ### Step-by-Step Solution - **Given**: Area of square $ABCD = 36$ sq. m. Area of rectangle $AEFG = 36$ sq. m. $E$ is the midpoint of $AB$. - First, find the side of square $ABCD$: $\text{Side} = \sqrt{36} = 6$ m. Thus, $AB = 6$ m. - Since $E$ is the midpoint of $AB$, the length $AE$ is half of $AB$: $AE = 6 / 2 = 3$ m. - $AE$ acts as one side (let's call it the length) of the rectangle $AEFG$. - We know the area of rectangle $AEFG = AE \times AG = 36$. - Substitute $AE = 3$: $3 \times AG = 36 \implies AG = 36 / 3 = 12$ m. - Now, calculate the perimeter of rectangle $AEFG$: - $\text{Perimeter} = 2 \times (AE + AG) = 2 \times (3 + 12)$ - $\text{Perimeter} = 2 \times 15 = 30$ m. ### Exam Strategy & Shortcut Once you see area $= 36$, side $= 6$. Midpoint means side is $3$. $3 \times \text{unknown} = 36 \implies \text{unknown} = 12$. Perimeter $= 2(12 + 3) = 30$. This logic chain can be executed entirely mentally in seconds. ### Common Pitfall Assuming the rectangle is fully contained within the square or making an assumption about its dimensions without using the explicitly given area of the rectangle. ### Final Answer Therefore, the correct answer is **30 m**.