Question

the length of a rectangle is 5 inches longer than twice the width and the area is 12 inches squared. Let l represent the length and w represent the width. What equation correctly models the situation?

Answer 1

Length = 8 inch , Width =
`(3)/(2)` , This equation models the situation

Explanation:

Given as ;

The Area of Rectangle is 12 inches²

The Length of Rectangle is 5 inches longer than twice the width

Let The Length = L inches

The Width = W inches

According to question ,

L = 5 + (2 × w )

∵ The Area of Rectangle = Length × width

Or, 12 inches² = [ 5 + (2 × w ) ] × w

Or, 12 inches² = 5 w +2 w²

Or, 2 w² + 5 w - 12 = 0

Or, 2 w² + 8 w -3 w - 12 = 0

Or, 2 w (w +4) - 3 (w + 4) = 0

I.e (w + 4) ( 2 w - 3) = 0

So , w = -4 , and w =
`(3)/(2)`

∴ Length = 5 + (2 × w ) =

Length = 5 + (2 ×
`(3)/(2)` )

so , L = 5 + 3 = 8

Hence Length = 8 inch , Width =
`(3)/(2)` This equation models the situation Answer