1. The length of a rectangle is 5.4 cm more than 3 times the width. If the perimeter of the rectangle is 80.4 cm, what are its dimensions? Please show your work.
Let's start by assigning variables to the dimensions of the rectangle:
Let the width be "w" cm.
Then the length is 3w + 5.4 cm (since it is 5.4 cm more than 3 times the width).
The formula for the perimeter of a rectangle is:
Perimeter = 2(length + width)
Substituting the given values into the formula:
80.4 = 2((3w + 5.4) + w)
Simplifying the equation:
80.4 = 2(4w + 5.4)
80.4 = 8w + 10.8
Subtracting 10.8 from both sides:
80.4 - 10.8 = 8w
69.6 = 8w
Dividing both sides by 8:
69.6/8 = w
8.7 = w
So the width of the rectangle is 8.7 cm.
Now, let's find the length:
length = 3w + 5.4
length = 3(8.7) + 5.4
length = 26.1 + 5.4
length = 31.5 cm
Therefore, the dimensions of the rectangle are:
Width = 8.7 cm
Length = 31.5 cm.
Let's call the width of the rectangle "x" cm.
According to the problem, the length of the rectangle is 5.4 cm more than 3 times the width, so the length is 3x + 5.4 cm.
The perimeter of a rectangle is given by the formula: Perimeter = 2(length + width).
Substituting the values, we have:
80.4 cm = 2(3x + 5.4 cm + x)
Simplifying the equation:
80.4 cm = 2(4x + 5.4 cm)
80.4 cm = 8x + 10.8 cm
80.4 cm - 10.8 cm = 8x
69.6 cm = 8x
x = 69.6 cm / 8
x = 8.7 cm
So the width of the rectangle is 8.7 cm.
Now we can find the length:
Length = 3x + 5.4 cm
Length = 3(8.7 cm) + 5.4 cm
Length = 26.1 cm + 5.4 cm
Length = 31.5 cm
Therefore, the dimensions of the rectangle are width = 8.7 cm and length = 31.5 cm.
To solve this problem, we can use the formulas for the perimeter and length of a rectangle.
Let's let the width of the rectangle be represented by "w," and the length be represented by "l."
1. We are given that the length of the rectangle is 5.4 cm more than 3 times the width. We can represent this as:
l = 3w + 5.4
2. The formula for the perimeter of a rectangle is:
P = 2l + 2w
We are also given that the perimeter is 80.4 cm, so we can substitute these values into the formula:
80.4 = 2(3w + 5.4) + 2w
3. Now, we can simplify and solve the equation for w:
80.4 = 6w + 10.8 + 2w
80.4 = 8w + 10.8
Subtracting 10.8 from both sides, we get:
69.6 = 8w
Dividing both sides by 8, we find:
w = 8.7
4. Now that we know the width is 8.7 cm, we can substitute this value back into the equation for the length:
l = 3w + 5.4
l = 3(8.7) + 5.4
l = 26.1 + 5.4
l = 31.5
Therefore, the dimensions of the rectangle are width = 8.7 cm and length = 31.5 cm.