A square is divided into three rectangles, A, B and C - OCR - GCSE Maths - Question 10 - 2017 - Paper 1

The area of rectangle A can be calculated using the formula for the area of a rectangle, which is:

$ext{Area} = ext{length} imes ext{width}$

Therefore, the area of rectangle A is:

$ext{Area of rectangle A} = n imes 2 = 2n ext{ cm}^2$

To find the value of n, we know that all rectangles have the same area. Let's denote the area of rectangle B which has a width of $(4 - n)$ and height of 2 cm:

$ext{Area of rectangle B} = (4 - n) imes 2 = 2(4 - n)$

Setting the areas equal (as all rectangles have the same area) gives us:

$2n = 2(4 - n)$

Dividing both sides by 2:

$n = 4 - n$

Rearranging the equation:

$2n = 4$

Thus, solving for n gives:

$n = 2$