CASE STUDY CHALLENGE

Matrices: School Land Plot

Rohini wants to give a rectangular plot of land for a school in her village. When asked about dimensions, she gave the following conditions:

Conditions given:

  • • If length is decreased by 50 m and breadth is increased by 50 m, the area remains the same.
  • • If length is decreased by 10 m and breadth is decreased by 20 m, the area decreases by 5300 sq m.

Let the length be x meters and breadth be y meters.

Answer the following:

(i) Write the system of linear equations in x and y based on the given information. [1]
(ii) Write the system of linear equations obtained in (i) in the matrix equation form AX = B. [1]
(iii) (a) Determine the inverse matrix A-1.

— OR —

(b) Find the area of the plot.

 [2]
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