Problem Statement for Picture Frame Program A piece of wire is to be bent in the form of a rectangle to put around a picture frame. The length of the picture frame is 1.5 times the width. Write a program that asks the user to enter the length of the wire and outputs the length and width of the picture frame. Part 1. Understand the ProblemThe problem gets the length of the wire for the frame from the user. The ratio of length to width of the frame is a constant (1.5). The length and width of the picture frame that are to be calculated and displayed. The length of wire represents the perimeter of the rectangular picture frame. The equation for the perimeter of a rectangle is: Perimeter = 2 * (length + width) This is an equation with two unknowns, but the ratio of the lengthto the width (length = ratio * width) so substitute for length in the perimeter equation and solve for width: Perimeter = 2 * (ratio * width + width) ratio * width + width = Perimeter / 2 width * (ratio + 1) = Perimeter / 2 width = Perimeter / (2 * (ratio+ 1))Calculate the length using this equation:length = ratio * width For this problem, the input is the perimeter (total length of the wire) and the outputs are the length and width of the frame. The order of calculations is important since the width must be calculated before the length can be calculated. To create a test case for the program, start with a known length and width, calculate the perimeter and then see if the program produces the original length and width when given the perimeter: Assume width = 6 so the length would be 6 * 1.5 = 9. The perimeter would be 2 * (6 + 9) = 30. Using the derived equations: ratio = 1.5 Perimeter = 30width = 30 / (2 * (1.5 + 1)) = 30 / (2 * 2.5) = 30 / 5 = 6 (good!) length = 6 * 1.5 = 9 So the program should produce a length of 9 and a width of 6 when given 30 for the perimeter (PYTHON)
Problem Statement for Picture Frame Program
A piece of wire is to be bent in the form of a rectangle to put around a picture frame. The length of the picture frame is 1.5 times the width. Write a program that asks the user to enter the length of the wire and outputs the length and width of the picture frame.
Part 1. Understand the ProblemThe problem
gets the length of the wire for the frame from the user. The ratio of length to width of the frame is a constant (1.5).
The length and width of the picture frame that are to be calculated and displayed.
The length of wire represents the perimeter of the rectangular picture frame. The equation for the perimeter of a rectangle is:
Perimeter = 2 * (length + width)
This is an equation with two unknowns, but the ratio of the lengthto the width (length = ratio * width) so substitute for length in the perimeter equation and solve for width:
Perimeter = 2 * (ratio * width + width)
ratio * width + width = Perimeter / 2
width * (ratio + 1) = Perimeter / 2
width = Perimeter / (2 * (ratio+ 1))Calculate the length using this equation:length = ratio * width
For this problem, the input is the perimeter (total length of the wire) and the outputs are the length and width of the frame. The order of calculations is important since the width must be calculated before the length can be calculated.
To create a test case for the program, start with a known length and width, calculate the perimeter and then see if the program produces the original length and width when given the perimeter:
Assume width = 6 so the length would be 6 * 1.5 = 9. The perimeter would be 2 * (6 + 9) = 30. Using the derived equations:
ratio = 1.5
Perimeter = 30width = 30 / (2 * (1.5 + 1)) = 30 / (2 * 2.5) = 30 / 5 = 6 (good!)
length = 6 * 1.5 = 9
So the program should produce a length of 9 and a width of 6 when given 30 for the perimeter
(PYTHON)
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