A square, with sides of length x cm, is inside a circle - Edexcel - GCSE Maths - Question 8 - 2017 - Paper 3

Since the vertices of the square are on the circumference of the circle, the diagonal of the square equals the diameter of the circle. The relationship between the side length x of the square and its diagonal d is given by:

$d = x\sqrt{2}$

The diameter d of the circle can also be expressed as:

$d = 2r \approx 2 \cdot 3.95 \approx 7.9 cm$

Setting these two expressions for d equal gives:

$x \sqrt{2} = 7.9$

Thus, we can solve for x:

$x = \frac{7.9}{\sqrt{2}} \approx 5.585$

Rounding the answer to 3 significant figures, we get:

$x \approx 5.59 cm$