1. The problem states that six identical right-angled triangles are arranged to form a rectangle. 2. The height of the rectangle is given as 7 cm. 3. Since the rectangle is made of 6 identical right-angled triangles, and they are arranged in two columns of 3 triangles each, the height of the rectangle corresponds to the combined height of 3 triangles. 4. Therefore, the height of one triangle is $\frac{7}{3}$ cm. 5. The length of the rectangle is twice the base of one triangle because two triangles are placed side by side to form the rectangle's length. 6. Let the base of one triangle be $b$ cm. Then the length of the rectangle is $2b$ cm. 7. Since the triangles are right-angled and identical, the base and height relate to the rectangle's dimensions. 8. The height of one triangle is $\frac{7}{3}$ cm, so the base of one triangle is also $\frac{7}{3}$ cm (because the triangles fit perfectly to form a rectangle). 9. Therefore, the length of the rectangle is $2 \times \frac{7}{3} = \frac{14}{3} = 4.67$ cm (rounded to two decimal places). Final answer: The length of the rectangle is approximately 4.67 cm.