Question

Use a product of two binomials to find a polynomial that represents the area of Roberto's plot.

Answer 1

Answer:

First, we know that the area of a rectangle of width W and length L is:

A = W*L

In the case of Roberto's plan, we can see that the length of the whole rectangle is:

L = 1.5ft + x + 1.5ft = 3 ft + x

And the width is:

W = 3ft + x + 3ft = 6ft + x

Then the area of the whole thing is:

A = (3ft + x)*(6ft + x)

This is what we wanted, a product of two polynomials that represents the area of Roberto's plot.

Now if we subtract the white square (is a square of sidelength x, then its area is A = x*x) we will get the area of the border;

The total area of Roberto's borders is:

Area of the border =  (3ft + x)*(6ft + x) - x*x

                               =   3ft*6ft + 3ft*x + x*6ft + x^2 - x^2

                               = x*9ft + 18ft^2