Question

Can anyone help me solve this please?

Answer 1

The linear equations for the given Rectangle are

1. 
   `y = 4x +4`
2. 
   `y = 6x - 6`

Explanation:

Given:

area given by 'y'

For figure 1,

`Length  = x +1\\Breadth = 4\\\textrm{Area of Rectangle} = Length* Breadth\\y= (x+1)* 4\\y= 4x + 4`

For figure 2,

`Length  = 2x -2\\Breadth = 3\\\textrm{Area of Rectangle} = Length* Breadth\\y= (2x-2)* 3\\y= 6x - 6`

Now we will plot the these two line on DESMOS so, we will have the intersection of these two line.

So, the intersection points are (5,24) that is x coordinate '5' and y coordinate '24'.

∴
`x=5\ and\ y=24`

For figure 1,

∴
`Length =x+1\\=5+1\\=6\ unit\\Area=4x + 4\\=4*5 +4\\=24\textrm{ square units}`

For figure 2,

∴
`Length =2x-2\\=2*5-2\\=8\ unit\\Area=6x - 6\\=6*5 -6\\=24\textrm{ square units}`