The diagram shows a square with four identical corners shaded - OCR - GCSE Maths - Question 25 - 2018 - Paper 1

The unshaded area can be determined by subtracting the shaded area from the area of the square:

$\text{Unshaded area} = \text{Area of square} - \text{Shaded area} = 9 - 2x^2$

Now we want to show that:

$\frac{\text{Shaded area}}{\text{Unshaded area}} = \frac{2}{7}$

This translates to:

$\frac{2x^2}{9 - 2x^2} = \frac{2}{7}$

Cross-multiplying gives:

$2x^2 \cdot 7 = 2(9 - 2x^2)$

Which simplifies to:

$14x^2 = 18 - 4x^2$

Adding (4x^2) to both sides results in:

$18x^2 = 18$

Dividing by 18 yields:

$x^2 = 1$

Thus concluding the relationship between the shaded and unshaded areas.