Length & Width Question

Question

Mary has a rectangular painting with a border that she is going to frame. The length of her painting is 5 inches longer than it’s width and the border is 2 inches around all sides of the painting.

1. Draw sketch to represent Mary’s painting and its border that will be framed. Your sketch must include information given.

2.Write an expression for the area of the frame.

3.write an expression for the perimeter of the frame.

*Questions 2 and 3 must be simplified and written in standard form.

Answer 1

So, to find the area of the frame, we find the area of the entire thing and subtract the area of the painting.

A_p = w(w + 5) = w² + 5w

Now, if the border is 2 inches all the way around, it adds 4 inches to both the length and the width. You should be able to see that in your sketch.

A_e = (w + 4)(w + 9) = w² + 13w + 36

A_f = w² + 13w + 36 - (w² + 5w) = 8w + 36

The perimeter of the frame is the distance around the outside.

P_f = 2(w + 4) + 2(w + 9) = 2w + 8 + 2w + 18 = 4w + 26