The sum of the area of rectangle A and B is 2964 cm ² . The ratio between the breadth of rectangle A and length of rectangle B is 2:3 respectively. The length of rectangle B is 9 cm less than the breadth of the same rectangle. If the perimeter of rectangle B is 174 cm, then find out the length of rectangle A.

Solution

The ratio between the breadth of rectangle A and length of rectangle B is 2:3 respectively. Let’s assume the breadth of rectangle A and length of rectangle B are 2y and 3y respectively. The length of rectangle B is 9 cm less than the breadth of the same rectangle. 3y = (breadth of rectangle B) - 9 breadth of rectangle B = (3y+9) If the perimeter of rectangle B is 174 cm. 2[3y+(3y+9)] = 174 [6y+9] = 87 6y = 87-9 6y = 78 y = 13 The sum of the area of rectangle A and B is 2964 cm ² . area of rectangle A + area of rectangle B = 2964 (length of rectangle A) x 2y + 3y x (3y+9) = 2964 Put the value of ‘y’ in the above equation. (length of rectangle A) x 2x13 + 3x13 x (3x13+9) = 2964 26x(length of rectangle A) + 39 x (39+9) = 2964 2x(length of rectangle A) + 3 x (39+9) = 228 2x(length of rectangle A) + 3 x 48 = 228 2x(length of rectangle A) + 144 = 228 2x(length of rectangle A) = 228-144 = 84 length of rectangle A = 42 cm