Boye cuts out a rectangle that has a perimeter of 26 inches and a length of 8 inches. He cuts out another rectangle that is the same length and twice as wide.
What is the perimeter of the new rectangle?
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inch(es)
Let's assume the width of the rectangle that Boye cuts out is "w" inches.
The perimeter of a rectangle is given by the formula P = 2l + 2w, where "l" is the length and "w" is the width.
Given that the length of the rectangle is 8 inches and the perimeter is 26 inches, we can set up the equation:
26 = 2(8) + 2w
Simplifying this equation gives us:
26 = 16 + 2w
Subtracting 16 from both sides, we have:
10 = 2w
Dividing both sides by 2, we get:
5 = w
So the width of the rectangle Boye cuts out is 5 inches.
Now let's find the dimensions of the new rectangle. The length remains the same at 8 inches, and the width is twice as wide as the original rectangle, so it is 2 * 5 = 10 inches.
The perimeter of the new rectangle is given by the formula P = 2l + 2w:
P = 2(8) + 2(10) = 16 + 20 = 36
Therefore, the perimeter of the new rectangle is 36 inches.
To find the perimeter of the new rectangle, we need to know the width of the rectangle. Since the length is given as 8 inches, we can find the width by using the given information that the new rectangle is twice as wide as the original rectangle.
Width of the new rectangle = Twice the width of the original rectangle = 2 * (Width of the original rectangle)
Let's find the width of the original rectangle first.
Perimeter of a rectangle is given by the formula:
Perimeter = 2 * (Length + Width)
Given that the perimeter of the original rectangle is 26 inches and the length is 8 inches, we can substitute these values into the formula to find the width of the original rectangle:
26 = 2 * (8 + Width)
26 = 16 + 2 * Width
Subtracting 16 from both sides:
10 = 2 * Width
Dividing both sides by 2:
Width = 5 inches
Now, we know the width of the original rectangle is 5 inches.
Using this information, we can find the width of the new rectangle:
Width of the new rectangle = 2 * Width of the original rectangle
= 2 * 5 inches
= 10 inches
Finally, to calculate the perimeter of the new rectangle:
Perimeter of the new rectangle = 2 * (Length + Width)
= 2 * (8 + 10) inches
= 2 * 18 inches
= 36 inches
Therefore, the perimeter of the new rectangle is 36 inches.
To find the perimeter of a rectangle, you add up the lengths of all its sides. In this case, we have two rectangles: the first one with a length of 8 inches and an unknown width, and the second one with the same length of 8 inches but twice as wide as the first one.
Let's find the width of the first rectangle. The perimeter of a rectangle is given by the formula P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
Since the perimeter of the first rectangle is given as 26 inches, we can substitute the values into the equation: 26 = 2(8) + 2W.
Simplifying the equation, we have: 26 = 16 + 2W.
To isolate W, we subtract 16 from both sides: 26 - 16 = 2W.
This gives us: 10 = 2W.
Dividing both sides by 2, we find that the width of the first rectangle is 5 inches.
Now, for the second rectangle, we know that its length is also 8 inches, and it is twice as wide as the first rectangle. Therefore, the width of the second rectangle is 2 * 5 = 10 inches.
To find the perimeter of the new rectangle, we will use the same formula: P = 2L + 2W, where L is the length and W is the width.
Substituting the values, we get: P = 2(8) + 2(10) = 16 + 20 = 36 inches.
Therefore, the perimeter of the new rectangle is 36 inches.