MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions
Problem
A rectangular plot of land has an area of 1800m2. The length of the plot exceeds twice its width by 10m.
(i) Take the width to be xm and express the length in terms of x. Hence form a quadratic equation in x that represents the given information.
(ii) Calculate the discriminant of this quadratic equation and comment on the nature of its roots.
(iii) Solve the quadratic equation obtained in part (i) and determine the dimensions of the plot correct to two decimal places.
(iv) Using your answer from part (iii), find the perimeter of the plot, again correct to two decimal places.