Question

45. Barney wants to frame a square picture of his dog. The frame he bought fits a picture

with a perimeter no greater than 96 cm. He plans to put a 2-cm blue border around the
picture. Determine the maximum dimensions that the picture can have.

Answer 1

Answer: Let's denote the side length of the square picture as "x". The perimeter of the square picture without the frame is then 4x, and the perimeter of the picture with the blue border is (x+4) (since there is a 2 cm border on each side of the picture).

The problem states that the perimeter of the picture with the blue border cannot exceed 96 cm. Therefore, we can set up the following inequality:

x + 4 ≤ 96/4

Simplifying, we get:

x + 4 ≤ 24

Subtracting 4 from both sides, we get:

x ≤ 20

So the maximum side length of the square picture without the frame is 20 cm. With the blue border, the picture will have dimensions of (20+4) by (20+4), or 24 by 24 cm.

Explanation: