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

Answer:

Length = 8 inch , Width = $\frac{3}{2}$ , This equation models the situation

Step-by-step 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 = $\frac{3}{2}$

∴  Length = 5 + (2 × w ) =

   Length = 5 + (2 ×$\frac{3}{2}$  )  

so ,  L = 5 + 3 = 8

Hence Length = 8 inch , Width = $\frac{3}{2}$   This equation models the situation Answer