rectangle length and width

Question

area of rectangle =120 sq meters the width is 3 meters longer than 1/3rd length. what is length and width.

Answer 1

Given

The area of the rectangle is 120 sq metres.

Let the length of a rectangle is x .

The width is 3 metres longer than 1 / 3rd length.

So the width of  the rectangle is ( x / 3 ) + 3.

The area of the rectangle = length * width.

120 = x * [( x / 3 ) + 3].

120 =  x * [ x + 9 ] / 3

120 =[ x ^2  + 9 x ] / 3

360 =[ x ^2  + 9 x ]

x ^2  + 9 x - 360 = 0

x ^2  + 24 x -15 x  - 360 = 0

x ( x  + 24 ) - 15 ( x  + 24 ) = 0

( x + 24) ( x - 15 ) = 0

Apply zero  property.

x + 24 = 0 and x - 15  = 0

x = - 24 and x = 15

Length measurent is always positive.

The length of a rectangle is 15 meters

Therefore the width of a rectangle is x / 3 + 3.

 = 15 / 3 + 3  = 5 + 3  = 8 meters

Solution :   The length of a rectangle is 15 meters and

the width of a rectangle is 8 meters.