Multiplication Identities - STD 9

Rectangle Length and Breadth Changed

Find length and breadth

Problem

If the length of a rectangle is increased by 3 metres and the breadth decreased by 2 metres, its area would decrease by 10 square metres. If the length is decreased by 2 metres and the breadth increased by 3 metres, the area would increase by 30 square metres. Find the length and breadth of the rectangle.

Length +3, Breadth -2

(l + 3)(b - 2) = lb - 10

Length -2, Breadth +3

(l - 2)(b + 3) = lb + 30

Step-by-Step Solution

Step 1: Expand both equations

(l + 3)(b - 2) = lb + 3b - 2l - 6 = lb - 10
(l - 2)(b + 3) = lb - 2b + 3l - 6 = lb + 30

Step 2: Simplify to get linear equations

From first: 3b - 2l - 6 + 10 = 0 → 2l - 3b = 4
From second: -2b + 3l - 6 - 30 = 0 → 3l - 2b = 36

Step 3: Solve the system

From first equation: l = (3b + 4)/2
Substitute in second: 3*(3b + 4)/2 - 2b = 36
Multiply by 2: 9b + 12 - 4b = 72
5b = 60 → b = 12 m
l = (3*12 + 4)/2 = 20 m

Length

20 m

Breadth

12 m