The diagram shows a cube - Edexcel - GCSE Maths - Question 19 - 2020 - Paper 3

In a cube, all edges are of equal length. Thus, the length of an edge can be expressed using the relation between the cube's edge length (let's denote it as ( a )) and the diagonal (( d )):

$d = a\sqrt{3}$

Given that ( AH ) is the diagonal, we substitute:

$11.25 = a \sqrt{3}$

To find ( a ), we rearrange:

$a = \frac{11.25}{\sqrt{3}}$

Calculating this gives:

$a \approx \frac{11.25}{1.732} \approx 6.5 ext{ cm}$

Thus, the lower bound for the length of an edge of the cube is approximately:

$a \approx 6.5 ext{ cm}$