Question

A person has a rectangular board 12 inches by 16 inches around what she wants to put a uniform border of shells if she hasn't of shells were border whose area is 128 square in determine the width of the Border

Answer 1

2 inches

Explanation:

Given that:

Dimensions of rectangular board = 12 inches by 16 inches

Area of uniform border around the rectangular board = 128 square inches

To find:

Width of the border = ?

Solution:

Let the width of the uniform border =
`x` inches

Now, there are two rectangular shapes after the addition of border.

One rectangle with the border, one without the board.

Area of border can be found by subtracting the area of board from the area of rectangle with the board.

Dimensions of the rectangle with the border = (12+2
`x`) inches by (16+2
`x`) inches

Area of rectangle = Length
`*` Width

So, area of border = ((12+2
`x`)
`*` (16+2
`x`)) - 16
`*` 12 = 128 square inches

`\Rightarrow 4x^2+56x+192-192=128\\\Rightarrow 4x^2+56x-128=0\\\Rightarrow x^2+14x-32=0\\\Rightarrow (x+16)(x-2)=0\\\Rightarrow x = 2, -16`

Width can not be negative, so possible value of width = 2 inches