The area of a rectangle increases by 200 sq. m, if the length is increased by 8 m and the breadth by 3 m. The area increases by 255 sq. m, if the length is increased by 3 m and breadth by 8 m. Find the length and the breadth of the rectangle.
Linear Equations
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Question

The area of a rectangle increases by 200 sq. m, if the length is increased by 8 m and the breadth by 3 m. The area increases by 255 sq. m, if the length is increased by 3 m and breadth by 8 m. Find the length and the breadth of the rectangle.

Linear Equations

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KnowledgeBoat · Accepted Answer

Let 'l' be the length of the rectangle and 'b' be the breadth of the rectangle. Area of the rectangle = length x breadth = lb When the length is increased by 8m and breadth by 3 m, area is increases by 200 sq.m, ⇒ (l + 8)(b + 3) = lb + 200 ⇒ l(b + 3) + 8(b + 3) = lb + 200 ⇒ lb + 3l + 8b + 24 = lb + 200 ⇒ 3l + 8b + 24 = 200 ⇒ 3l + 8b = 200 - 24 ⇒ 3l + 8b = 176.................(1) When the length is increased by 3m and breadth by 8m, area is increases by 255 sq.m, ⇒ (l + 3)(b + 8) = lb + 255 ⇒ l(b + 8) + 3(b + 8) = lb + 255 ⇒ lb + 8l + 3b + 24 = lb + 255 ⇒ 8l + 3b + 24 = 255 ⇒ 8l + 3b = 255 - 24 ⇒ 8l + 3b = 231 ...............(2) Solving the equation (1) and (2), we get ⇒ (3l + 8b = 176) x 8 (8l + 3b = 231) x 3 ⇒ b = ⇒ b = 13 From equation (1), we get: ⇒ 3l + 8 x 13 = 176 ⇒ 3l + 104 = 176 ⇒ 3l = 176 - 104 ⇒ 3l = 72 ⇒ l = ⇒ l = 24 Hence, the length of the rectangle = 24 m and the breadth of the rectangle = 13 m.

Mathematics

The area of a rectangle increases by 200 sq. m, if the length is increased by 8 m and the breadth by 3 m. The area increases by 255 sq. m, if the length is increased by 3 m and breadth by 8 m. Find the length and the breadth of the rectangle.

Linear Equations

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