Rectangles are drawn on line segments of fixed lengths When the breadths are 6 m and 5 m respectivel...

Question

Rectangles are drawn on line segments of fixed lengths. When the breadths are 6 m and 5 m

respectively the sum of the areas of the rectangles is 83 m². But if the breadths are 5 m and 4 m

respectively the sum of the areas is 68 m². Find the sum of the areas of the squares drawn on the

line segments.

Accepted Answer

Lets consider the length of the room as x meter And the breadth of the room y meter So the area of the room length x breadth xy sq meter Now according to the first condition given in the problem we have xy x 1 y 1 1 21 xy xy x y 1 21 x y 20 i And according to the second condition we have xy x 1 y 2 14 xy xy y 2x 2 14 2x y 16 ii Adding i and ii we get x y 20 2x y 16 3x 36 x 363 x 12 On substituting the value of x in equation i we get 12 y 20 y 20 12 y 8 Thus the length of the room 12 m and the breadth of the room 8 m Therefore the perimeter of the room 2 x length breadth 2 x 12 8 2 x 20 40 m

ML Aggarwal Solutions Class 9 Mathematics Solutions for Problems on Simultaneous Linear Equations Exercise 6 in Chapter 6 - Problems on Simultaneous Linear Equations