(a) see diagram above Let a side of the rhombus be n. Then \(n^{2} = 4.65^{2} + 5.1^{2}\) = \(21.6225 + 26.01 \) \(n^{2} = 47.6325\) \(n = \sqrt{47.6325} = 6.902 cm\) Hence, the perimeter of the rhombus = 4n = \(4 \times 6.902\) = \(27.608 cm \approxeq 27.6 cm\) (to 1 d.p) (b) Right-angled triangle ABC see diagram above \(\sin x = \frac{3}{5}\), Thus, \(m^{2} = 5^{2} - 3^{2} = 25 - 9 = 16\) \(m = 4\). \(\cos x = \frac{4}{5} \implies 5\cos x = 5 \times \frac{4}{5} = 4\) \(\tan x = \frac{3}{4} \implies 4\tan x = 4 \times \frac{3}{4} = 3\) \(5\cos x - 4\tan x = 4 - 3 = 1\).