IGCSE Mathematics 0580/04/SP/20 Q5
5 (a) The perimeter of the rectangle is 80 cm. The area of the rectangle is A cm2.
(i) Show that x2 – 40x + A = 0.
(ii) When A = 300, solve the equation x2 – 40x + A = 0 by factorising.
(iii) When A = 200, solve the equation x2 – 40x + A = 0 using the quadratic formula. Show all your working and give your answers correct to 2 decimal places.
(b) A car completes a 200 km journey at an average speed of x km/h.
The car completes the return journey of 200 km at an average speed of (x + 10) km/h.
(i) Show that the difference between the time taken for each of the two journeys is 2000/x(x + 10) hours.
(ii) Find the difference between the time taken for each of the two journeys when x = 80. Give your answer in minutes and seconds.