Question

The width of a rectangle is (x+1) and the length is (x-6). What is the length and width of the rectangle if the area is 30 square feet?

Answer 1

Answer:

The length of the rectangle (l) = 3 feet

The width of the rectangle (W) =  10 feet

Step-by-step explanation:

Step(i):-

Given that the width of the rectangle  = (x+1) feet

Given that the length of the rectangle = ( x-6) feet

The area of the rectangle = 30 square feet

Step(ii):-

We know that the area of the rectangle

                = length ×width

    30   = ( x+1)(x-6)

    30   = x² - 6x + x -6

⇒ x² - 5 x - 6 = 30

⇒ x² - 5 x - 6 - 30 =0

⇒ x² - 5 x - 36 =0

 x² - 9 x +4x - 36 =0

   x (x-9) +4 ( x-9) =0

   ( x+4 ) ( x-9) =0

     ( x+4 ) =0 and  ( x-9) =0

     x =-4 and x =9

Step(iii):-

we have to choose x =9

     The length of the rectangle (l) =  x-6 = 9-6 =3

      The width of the rectangle (W) =  x+1 =  9 +1 = 10

Final answer:-

The length of the rectangle (l) = 3 feet

The width of the rectangle (W) =  10 feet