rectangles length is 3 more than twice its width and has a perimeter of 30 centimeters find the dimensions
P = 2L + 2W
30 = 2(2W + 3) + 2W
30 = 4W + 6 + 2W
24 = 6W
24/6 = W
4 = W
Well, well, well. It seems we have some rectangular mischief going on here. Let's unravel this conundrum, shall we?
Let's call the width of our rectangular clown, I mean rectangle, "w". Now, according to the riddle, the length is 3 more than twice the width. So, that means the length is 2w + 3.
To find the perimeter, we add up all the sides. For a rectangle, you have two sides that are equal to the width, and two sides that are equal to the length. That gives us the equation:
2w + 2(2w + 3) = 30
Now, let's solve it like a puzzle. Simplify and combine like terms:
2w + 4w + 6 = 30
Combine terms again:
6w + 6 = 30
Now, let's subtract 6 from both sides:
6w = 24
And divide both sides by 6:
w = 4
Voila! The width is 4 centimeters.
But hold your clown nose, we're not done yet. Plug this value back into our equation for the length:
2w + 3 = 2(4) + 3 = 8 + 3 = 11
So, the length of our clownish rectangle is 11 centimeters.
Therefore, the dimensions of our rectangular rascal are a width of 4 centimeters and a length of 11 centimeters.
Let's assume the width of the rectangle is 'w' centimeters. According to the given information, the length of the rectangle is 3 more than twice its width, which can be expressed as:
Length = 2w + 3
The formula for the perimeter of a rectangle is:
Perimeter = 2(length + width)
Given that the perimeter is 30 centimeters, we can set up the equation:
30 = 2(2w + 3 + w)
Now we can solve for 'w':
30 = 2(3w + 3)
30 = 6w + 6
24 = 6w
w = 4
So, the width of the rectangle is 4 centimeters.
Now, we can find the length:
Length = 2w + 3
Length = 2(4) + 3
Length = 8 + 3
Length = 11
Therefore, the dimensions of the rectangle are 4 cm (width) and 11 cm (length).
To find the dimensions of the rectangle, we need to set up a system of equations using the given information.
Let's assume the width of the rectangle is "w" centimeters.
According to the problem, the length of the rectangle is 3 more than twice its width, which can be expressed as:
Length = 2w + 3
The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width)
Substituting the given values into the formula, we have:
30 = 2(2w + 3 + w)
Simplifying the equation, we get:
30 = 2(3w + 3)
Next, distribute the 2:
30 = 6w + 6
Now, isolate the variable:
30 - 6 = 6w
24 = 6w
Finally, divide both sides by 6:
w = 4
So, the width of the rectangle is 4 centimeters.
Now, we can find the length using the formula we derived earlier:
Length = 2w + 3
Length = 2(4) + 3
Length = 8 + 3
Length = 11
Therefore, the dimensions of the rectangle are width = 4 centimeters and length = 11 centimeters.