Question

2) The breadth of a rectangle is 3 less than the length. If both length and breadth are reduced by
3 units, the area of the rectangle reduces by 90 sq. units. Find the dimensions of the original
rectangle.​

Answer 1

Answer

Length of the rectangle = 18 cm

Breadth of the rectangle = 15 cm

Area of the rectangle = 270 cm²

Given

The breadth of a rectangle is 3 less than the length. If both the length and the breadth are reduced by 3 units, the area of the rectangle reduces by 90 sq. units.

To Find

Dimensions of original rectangle

 Area of rectangle = Length × Breadth

⇒ A = lb

Solution

Let the length of the rectangle be , " x "

Breadth be , " y "

A/c , " The breadth of a rectangle is 3 less than the length "

⇒ y = x - 3

⇒ x - y = 3 ... (1)

Area of the rectangle = xy

A/c , " If both the length and the breadth are reduced by 3 units, the area of the rectangle reduces by 90 sq. units "

⇒ ( x - 3 )( y - 3 ) = xy - 90

⇒ xy - 3x - 3y + 9 = xy - 90

⇒ 3x + 3y = 99

⇒ x + y = 33 ... (2)

Solve (1) + (2) ,

⇒ ( x - y ) + ( x + y ) = 3 + 33

⇒ x - y + x + y = 36

⇒ 2x = 36

⇒ x = 18 cm

On sub. x value in (1) , we get ,

⇒ (18) - y = 3

⇒ y = 18 - 3

⇒ y = 15 cm

So , Area of the rectangle = xy = 270 cm²

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