Elena cuts out a rectangle that has a perimeter of 156 inches and a length of 45 inches. She cuts out another rectangle that is the same length and twice as wide.
What is the perimeter of the new rectangle? 9
inch(es)
The first rectangle has a length of 45 inches.
We know that the formula for the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
Let's call the width of the first rectangle x inches.
Therefore, the perimeter of the first rectangle can be written as 2(45) + 2x = 90 + 2x.
We are given that the perimeter of the first rectangle is 156 inches, so we can write the following equation:
90 + 2x = 156.
Subtracting 90 from both sides, we get:
2x = 66.
Dividing both sides by 2, we have:
x = 33 inches.
So, the first rectangle has a width of 33 inches.
To find the dimensions of the second rectangle, we know that it has the same length (45 inches) and twice the width.
Therefore, the width of the second rectangle is 2 * 33 = 66 inches.
The perimeter of the second rectangle can be calculated as 2(45) + 2(66) = 90 + 132 = 222 inches.
Thus, the perimeter of the new rectangle is 222 inches.
To find the perimeter of the new rectangle, we need to determine its length and width.
Given that the length of the new rectangle is the same as the first rectangle, which is 45 inches, and the new rectangle is twice as wide, we can calculate its width.
Width of the new rectangle = 2 * width of the first rectangle
Let's call the width of the first rectangle 'w1'.
So, width of the new rectangle = 2 * w1
To find the perimeter of the new rectangle, we use the formula:
Perimeter = 2 * (length + width)
Given that the length of the new rectangle is 45 inches and the width is 2 * w1, we can substitute these values into the formula to find the perimeter.
Perimeter of the new rectangle = 2 * (45 + 2 * w1)
To find the perimeter of the new rectangle, we need to know the dimensions of the rectangle. Let's calculate the width of the new rectangle first.
We are given that the length of the new rectangle is the same as the length of the original rectangle, which is 45 inches.
The original rectangle has a perimeter of 156 inches, which means its width plus length plus width plus length equals 156 inches. So, we can set up the equation:
2(width) + 2(45 inches) = 156 inches
Simplifying the equation:
2(width) + 90 inches = 156 inches
2(width) = 156 inches - 90 inches
2(width) = 66 inches
(width) = 66 inches / 2
(width) = 33 inches
Therefore, the width of the new rectangle is 33 inches.
Now that we know the length and width of the new rectangle (45 inches and 33 inches respectively), we can calculate its perimeter:
Perimeter = 2(length) + 2(width)
Perimeter = 2(45 inches) + 2(33 inches)
Perimeter = 90 inches + 66 inches
Perimeter = 156 inches
So, the perimeter of the new rectangle is 156 inches.