The area of rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. However, if the length of this rectangle increases by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
Linear Equations
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Question

The area of rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. However, if the length of this rectangle increases by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

Linear Equations

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KnowledgeBoat · Accepted Answer

Let the length of rectangle be x units and breadth be y units. Given, Area of rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. ⇒ (x - 5)(y + 3) = xy - 9 ⇒ xy + 3x - 5y - 15 = xy - 9 ⇒ xy - xy + 3x - 5y = -9 + 15 ⇒ 3x - 5y = 6 ........(1) Given, If the length of this rectangle increases by 3 units and the breadth by 2 units, the area increases by 67 square units. ⇒ (x + 3)(y + 2) = xy + 67 ⇒ xy + 2x + 3y + 6 = xy + 67 ⇒ xy - xy + 2x + 3y = 67 - 6 ⇒ 2x + 3y = 61 ........(2) Multiplying equation (1) by 2, we get : ⇒ 2(3x - 5y) = 2 × 6 ⇒ 6x - 10y = 12 .........(3) Multiplying equation (2) by 3, we get : ⇒ 3(2x + 3y) = 3 × 61 ⇒ 6x + 9y = 183 .........(4) Subtracting equation (3) from (4), we get : ⇒ (6x + 9y) - (6x - 10y) = 183 - 12 ⇒ 6x - 6x + 9y + 10y = 171 ⇒ 19y = 171 ⇒ y = = 9. Substituting value of y in equation (1), we get : ⇒ 3x - 5(9) = 6 ⇒ 3x - 45 = 6 ⇒ 3x = 45 + 6 ⇒ 3x = 51 ⇒ x = = 17. Hence, length = 17 units and breadth = 9 units.

Mathematics

The area of rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. However, if the length of this rectangle increases by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

Linear Equations

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