(a) \((PT)^{2} + (TQ)^{2} = (PQ)^{2}\) \((PT)^{2} + 6^{2} = 10^{2}\) \((PT)^{2} = 100 - 36 = 64\) \(\therefore PT = 8 cm\) \(\therefore \frac{8}{6} = \frac{14.4}{SR}\) \(SR = \frac{6 \times 14.4}{8}\) \(SR = 10.8 cm\) Area of the quadrilateral QRST = \(\frac{1}{2} (6 + 10.8) \times 6.4\) = \(53.76 cm^{2}\) (b) Opp sides of a square = \((\frac{(100 - 10)x}{100} = 0.9x\) other two sides of the square = \(\frac{(100 + 15)x}{100} = 1.15x\) Area of the square : \(x \times x = x^{2}\) Area of the rectangle : \(0.9x \times 1.15x = 1.035x^{2}\) \(\therefore \text{The ratio of the area of the rectangle to the square} = 1.035x^{2} : x^{2}\) = \(1.035 : 1\)