Question

The length of a rectangle exceeds its width by 3 m. If the width is
increased by 4 m and the length is decreased by 6 m, the area is
decreased by 22 sq. m. Find the dimensions of the rectangle.​

Answer 1

Solution :-

Let the breath of rectangle be x

According to question,

The length of a rectangle exceeds its width by 3m

Therefore,

Length of rectangle = x + 3

Area of rectangle = Length * Breath

Area of rectangle = x ( x + 3 )

Area of rectangle = x^2 + 3x

Now, If the width is increased by 4m so the length is decreased by 6m

Length = ( x + 3 ) - 6

Length = x - 3

Breath = x + 4 ( According to the question)

Therefore,

Area of rectangle = Length * Breath

Area of rectangle = ( x - 3) ( x + 4)

Area of rectangle = x ( x + 4) -3( x + 4)

Area of rectangle = x^2 + 4x -3x -12

Area of rectangle = x^2 + x - 12

Now, we are given that area is decreased by 22sq. m

x^2 + x - 12 = x^2 + 3x -22

x - 3x = -22 + 12

-2x = -10

x = -10 / -2

x = 5

Therefore,

Breath ( x) = 5m

Length ( x + 3) = 5 + 3 = 8m

Answer 2

Answer:

Explanation:

Let the breadth of the rectangle be y

We are also given that The length of a rectangle exceeds its width by 3m

So, length = y+3

Area of rectangle = Length \times Breadth

Now we are given that the width is increased by 4 m and the length is decreased by 6 m

So,he length of the rectangle is y+3-6=y-3

So, the breadth of the rectangle is y+4

inSo, Area of rectangle = Length \times BreadthLength×Breadth= (y-3)(y+4)(y−3)(y+4)

= y^2+4y-3y-12

y2+4y−3y−12

= y^2+y-12y 2 +y−12