Question

The area of a rectangle gets reduced by 9 square units if its length is reduced by 5 units and the breadth is increased by 3 units if we increase the length by 3 units and the breadth by 2 units then the area is increased by 67 square units find the dimensions of the rectangle.

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Answer 1

length = 17 units, breadth = 9 units

Step-by-step explaination:-

Let the length and the breadth of the rectangle be x units and y units respectively.

Then the area of rectangle = xy square units

According to given conditions, we have

(x -5)(y + 3) = xy - 9 and (x + 3)(y + 2) = xy + 67

=> xy + 3x - 5y - 15 = xy - 9

and xy + 2x + 3x + 6 = xy + 67

=> 3x - 5y - 6 = 0......eqn(i)

and 2x + 3y - 61 = 0.....eqn(ii)

Multiplying equation (i) by 2 and equation (ii) by 3, we get...

6x - 10y - 12 = 0....eqn(iii) and,

6x + 9y - 183 = 0....eqn(iv)

Subtracting equation (iii) from equation (iv), we get...

19y - 171 = 0 => y = 9.

Substituting this value of y in equation (ii), we get

2x + 3 × 9 - 61. = 0 => 9x - 34 = 0 => x = 17.

Hence, the length of rectangle = 17 units and

breadth = 9 units.

Hope it helps you!!