Question

The length of a rectangle is 1 m greater than its width. If the length is increased by 2 m and the width is decreased by 6 m. the area decreases by 50 m^2. What are the dimensions of the rectangle?​

Answer 1

Answer:

The dimensions of rectangle is 8 m.

Step-by-step explanation:

Let the length of a rectangle is x + 1 m

Let the width of a rectangle is x m.

∴ Area of rectangle =(x+1)(x) m

                                 = x²+x m²

If the length of a rectangle is increased by 2=(x + 2) m

If the width of a rectangle is decreased by 6=(x -6)m

                              ∴Area of rectangle = (x +2)(x-6)

                                                                =x²-6x+3x-18

                                                                 = x²-3x-18 m²

Now , according to the question

⇒  x²-3x-18=x²+x-50   (∵cancel out x²)

⇒x-50+3x-18=0

⇒4x=32

⇒x = 8

  ∴ The dimensions of the rectangle is 8 m .