To help you find the perimeter and area of the original rectangle and the dilated rectangle, I will need the dimensions (length and width) of the original rectangle. If you provide those values, I can perform the calculations for you.
The rectangle below is dilated by a scale factor of 55. Find the perimeter and area of the rectangle below, as well as the perimeter and area of the dilated rectangle. Express your answers as whole numbers, decimals, or fractions in simplest terms (no mixed numbers). Figures are not necessarily drawn to scale.
Perimeter of given rectangle ? units
Area of given rectangle ? units2
Perimeter of dilated rectangle ? units
area of dilated rectangle ? units2
9 answers
The rectangle below is dilated by a scale factor of one quarter Find the perimeter and area of the rectangle below, as well as the perimeter and area of the dilated rectangle. Express your answers as whole numbers, decimals, or fractions in simplest terms (no mixed numbers). Figures are not necessarily drawn to scale.
To find the perimeter and area of both the original rectangle and the dilated rectangle by a scale factor of one quarter, we will use the following formulas:
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Perimeter of a Rectangle: \[ P = 2 \times (\text{length} + \text{width}) \]
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Area of a Rectangle: \[ A = \text{length} \times \text{width} \]
Step 1: Original Rectangle Dimensions
Since you have not provided the dimensions of the original rectangle, I’ll assume possible values for demonstration purposes. Let's say:
- Length = \(L\)
- Width = \(W\)
Step 2: Calculating the Original Rectangle's Perimeter and Area
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Perimeter of the original rectangle: \[ P_{\text{original}} = 2 \times (L + W) \]
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Area of the original rectangle: \[ A_{\text{original}} = L \times W \]
Step 3: Applying the Scale Factor
When the rectangle is dilated by a scale factor of \( \frac{1}{4} \), the new dimensions will be:
- New Length = \( \frac{L}{4} \)
- New Width = \( \frac{W}{4} \)
Step 4: Calculating the Dilated Rectangle's Perimeter and Area
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Perimeter of the dilated rectangle: \[ P_{\text{dilated}} = 2 \times \left(\frac{L}{4} + \frac{W}{4}\right) = 2 \times \frac{1}{4} \times (L + W) = \frac{1}{2} \times (L + W) \]
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Area of the dilated rectangle: \[ A_{\text{dilated}} = \left(\frac{L}{4}\right) \times \left(\frac{W}{4}\right) = \frac{L \times W}{16} \]
Step 5: Summary of Calculations
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Original Rectangle:
- Perimeter: \(2(L + W)\)
- Area: \(L \times W\)
-
Dilated Rectangle:
- Perimeter: \(\frac{1}{2} \times (L + W)\)
- Area: \(\frac{L \times W}{16}\)
If you provide the specific dimensions \(L\) and \(W\), I can compute specific numerical values for the perimeter and area of both the original and the dilated rectangle.
what are the total element and total atoms of C6H5CHO
The molecular formula \( \text{C}_6\text{H}_5\text{CHO} \) represents a compound known as benzaldehyde, which is an aromatic compound.
Total Elements
The total unique elements in the molecular formula are:
- Carbon (C)
- Hydrogen (H)
- Oxygen (O)
So there are 3 different types of elements in \( \text{C}_6\text{H}_5\text{CHO} \).
Total Atoms
Now, let's count the number of each atom in the formula:
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Carbon (C): There are 6 carbon atoms from \( C_6 \), and 1 carbon atom from \( CHO \). Total C = 6 + 1 = 7
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Hydrogen (H): There are 5 hydrogen atoms from \( H_5 \), and 1 hydrogen from \( CHO \). Total H = 5 + 1 = 6
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Oxygen (O): There is 1 oxygen atom from \( CHO \). Total O = 1
Adding these together, we have:
- Total C = 7
- Total H = 6
- Total O = 1
Summary
- Total unique elements: 3 (C, H, O)
- Total atoms: 7 (C) + 6 (H) + 1 (O) = 14 atoms total
Therefore, the total number of atoms in \( \text{C}_6\text{H}_5\text{CHO} \) is 14.
what are the total element and total atoms of MgCO3
The molecular formula \( \text{MgCO}_3 \) represents magnesium carbonate.
Total Elements
The unique elements in the molecular formula are:
- Magnesium (Mg)
- Carbon (C)
- Oxygen (O)
So there are 3 different types of elements in \( \text{MgCO}_3 \).
Total Atoms
Now, let's count the number of each atom in the formula:
-
Magnesium (Mg): There is 1 atom of magnesium.
- Total Mg = 1
-
Carbon (C): There is 1 atom of carbon.
- Total C = 1
-
Oxygen (O): There are 3 atoms of oxygen.
- Total O = 3
Adding these together, we have:
- Total Mg = 1
- Total C = 1
- Total O = 3
Summary
- Total unique elements: 3 (Mg, C, O)
- Total atoms: 1 (Mg) + 1 (C) + 3 (O) = 5 atoms total
Therefore, for \( \text{MgCO}_3 \):
- Total elements: 3
- Total atoms: 5
what are the total elements and total atoms of NaHCO3
The molecular formula \( \text{NaHCO}_3 \) represents sodium bicarbonate (also known as baking soda).
Total Elements
The unique elements in the molecular formula are:
- Sodium (Na)
- Hydrogen (H)
- Carbon (C)
- Oxygen (O)
So there are 4 different types of elements in \( \text{NaHCO}_3 \).
Total Atoms
Now, let's count the number of each atom in the formula:
-
Sodium (Na): There is 1 atom of sodium.
- Total Na = 1
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Hydrogen (H): There is 1 atom of hydrogen.
- Total H = 1
-
Carbon (C): There is 1 atom of carbon.
- Total C = 1
-
Oxygen (O): There are 3 atoms of oxygen.
- Total O = 3
Adding these together, we have:
- Total Na = 1
- Total H = 1
- Total C = 1
- Total O = 3
Summary
- Total unique elements: 4 (Na, H, C, O)
- Total atoms: 1 (Na) + 1 (H) + 1 (C) + 3 (O) = 6 atoms total
Therefore, for \( \text{NaHCO}_3 \):
- Total elements: 4
- Total atoms: 6
5 answers