## 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 *x*2 – 40*x *+ *A *= 0.

**(ii) **When *A *= 300, solve the equation *x*2 – 40*x *+ *A *= 0 by factorising**.**

**(iii) **When *A *= 200, solve the equation *x*2 – 40*x *+ *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.**

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