# The area of a rec

Area of a rectangle = l × b

Given, area of a rectangle remains the same if the length is increased by 7 metres and the breadth is decreased by 3 metres.
If the length is decreased by 7 metres and breadth is increased by 4 metres, the area is decreased by 21 sq. metres.

(l + 7)(b – 3) = lb

lb - 3l + 7b - 21 = lb

7b – 3l = 21 ------ (1)

Also, (l – 7)(b + 4) = lb - 21

lb + 4l - 7b - 28 = lb - 21

4l – 7b = 7 ------- (2)

Adding (1) and (2), we get

7b - 3l + 4l - 7b = 21 + 7

l = 28 m

put the value of l in 1 to get

7b - 3(28) = 21

Thus, 7b – 84 = 21

7b = 21 + 84

7b = 105

b = 15 m

Hence the length is 28 m and breadth is 15 m.

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