Question

the area of a rectangle reduced by 20 metre square if it's length is increased by 1 metre and the breadth is reduced by 2 the area increased by 12 square if the length is reduced by 3 metre and the breadth is increased by 4 metre find the dimension of the rectangle

Answer 1

The dimensions of the rectangle are 15 m and 12 m.

• Let l, b be the dimensions of the rectangle.

Case 1:

Length increased by 1 m

Breadth reduced by 2 m

Area (lb) reduced by 20 sq. m.

⇒ (l + 1)(b - 2) = lb - 20

⇒ lb - 2l + b - 2 = lb - 20

⇒- 2l + b = - 18

⇒ 2l - b = 18 -------------------(1)

Case 2:

Length reduced by 3 m

Breadth increased by 4m

Area (lb) increased by 12 sq m

⇒ (l - 3)(b + 4) = lb + 12

⇒ lb + 4l - 3b - 12 = lb + 12

⇒ 4l - 3b = 24   -------------------(2)

Solving (1) and (2)  , we get

l = 15 m, b = 12 m      

Refer attachment for solving part

Answer 2

Answer:

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