If the length of a rectangle is 5 m more than its width find the values of length and width if the area of a rectangle is 500 m²

Length of the rectangle  =25

width of the rectangle  = 20

Step-by-step explanation:

Step(i):-

Let 'x' be the width of the rectangle

Given that the length of a rectangle is 5 m more than its width

Given that Area of the rectangle = 500m²

length of a rectangle = x +5

width of a rectangle = x

Step(ii):-

Area of the rectangle = length × width

             500 = x ( x+5)

          x² + 5 x = 500

      ⇒  x² + 5 x - 500 =0

      ⇒  x² +25x - 20 x - 500 =0

    ⇒  x( x+25) -20(x+25) =0

  ⇒  (x-20)(x+25) =0

 ⇒  x =20 and x=-25

we can choose x =20

Step(iii):-

Length of the rectangle = x +5 = 20 +5 =25

width of the rectangle  = 20

Final answer:-

Length of the rectangle  =25

width of the rectangle  = 20