Question

A gardener has a rose garden that measures 30 feet by 20 feet. He wants to put a uniform border of pine bark around the outside of the garden. Let x be the width of the border in feet. Write an expression for the total area of the border in terms of the width x.

Answer 1

4x² +100x

Explanation:

The total area of the garden plus the pine bark border is given by:

`A = (30+2x)*(20+2x) = 600+60x +40x +4x^2`

The area of the garden alone, without the border, is:

`A_G = 30*20=600`

Subtracting the total area by the area of the garden gives us the area of the border:

`A_B = A -A_G\\A_B= 600+100x+4x^2 - 600\\A_B = 4x^2 +100x`

The total area of the border is described by 4x² +100x.