Mary is a public Mary is a public safety engineer She is pla

Mary is a public safety engineer. She is planning the layout of a farmers\' market. The market is to take place in a rectangular area that is twice as long as it is wide. On either side along the length of the rectangle. She wants to have four foot wide walkways (see the picture below). Suppose x is the width of the rectangle (in feet). What is the expression that represents the area allocated for the farmers\' market? If the expression is written in the format ax^2 + bx, what are the values of a and b

Solution

The total area is given by length x breadth i.e. x(2x)

So the total area is 2x²

The area of each walkway is 4(2x) that is 8x

There are two walkways so total area of walkways is 2(8x) that is 16x

So the area allocated to farmers\' market is total area - area of walkway

That is 2x²-16x

Therefore a is 2 and b is -16