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

For a square inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. The diagonal can be represented as:

$d = x\sqrt{2}$

And since the diameter is twice the radius:

$d = 2r$

Setting these equal gives:

$x\sqrt{2} = 2r$

From this equation, we can express x in terms of r:

Substituting the expression for r from the previous step:

$x\sqrt{2} = 2\sqrt{\frac{49}{\pi}}$

Rearranging to isolate x gives us:

$x = \frac{2\sqrt{49 / \pi}}{\sqrt{2}}$

Now we can simplify this expression.

Calculating the value, we find:

$x = \frac{14}{\sqrt{2\pi}}\approx 3.54$

Thus, rounding to three significant figures, the value of x is approximately 3.54 cm.