What can be concluded about a rectangle's width if the ratio of length to perimeter is 1 to 3? Make some sketches and explain your reasoning.
2 L + 2 b = perimeter
L/p = L/(2L+2b) = 1/3
3 L = 2L + 2 b
L = 2 b
the width is half the length
L/P=L/(2W+2L)=1/3. Cross multiply
and solve for W: 2W+2L=3L, 2W=3L-2L,
2W=L, W=L/2. CONCLUSION:The width is
1/2 of the Length.
Sketch a rectangle and L=4, W=2.
L/P SHOULD EQUAL1/3. CHECK:L/(2W+2L)=
4/(4+8)=1/3.
To determine the width of a rectangle, we can start by understanding the given ratio of the length to the perimeter.
The ratio of length to perimeter is 1:3. This means that if we take the length as 1 unit, the perimeter would be 3 units.
Let's make a sketch of a rectangle to visualize this information. Assume the length of the rectangle is represented by a line segment of length 1 unit.
To find the perimeter, we need to consider that the rectangle has two equal lengths (1 unit) and two equal widths (unknown length).
Using the formula for the perimeter of a rectangle (P = 2 * (length + width)), we know that the perimeter is equal to 3 units.
Therefore, we can set up the equation: 3 = 2 * (1 + width).
Now we can solve for the width by simplifying the equation:
3 = 2 + 2 * width
1 = 2 * width
width = 1/2
So, in this case, the width of the rectangle would be 1/2 unit.
However, it is important to note that this conclusion is based on the assumption that the ratio of length to perimeter is fixed for all rectangles. If the ratio for a specific rectangle differs, we would need additional information to determine its width.