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Answer :
To solve this problem, we need to find the height of different rectangles that all have the same area as an original rectangle. Here's how you can do that step by step:
1. Identify the original rectangle's measurements:
- The base (width) of the original rectangle is 18 centimeters.
- The height of the original rectangle is 2 centimeters.
2. Calculate the area of the original rectangle:
- The area of a rectangle can be calculated using the formula:
[tex]\[
\text{Area} = \text{base} \times \text{height}
\][/tex]
- For the original rectangle, the area is:
[tex]\[
\text{Area} = 18 \, \text{cm} \times 2 \, \text{cm} = 36 \, \text{cm}^2
\][/tex]
3. Write down the new base lengths given for the other rectangles:
- The new bases are 5 cm, -1 cm, 6 cm, 10 cm, and 36 cm.
4. Calculate the height for each of the new rectangles:
- Since all new rectangles must have the same area as the original (36 cm²), we can use the formula:
[tex]\[
\text{Height} = \frac{\text{Area}}{\text{base}}
\][/tex]
- Using this formula, calculate each height:
- For a base of 5 cm:
[tex]\[
\text{Height} = \frac{36}{5} = 7.2 \, \text{cm}
\][/tex]
- For a base of -1 cm (usually not practical, just theoretical):
[tex]\[
\text{Height} = \frac{36}{-1} = -36 \, \text{cm}
\][/tex]
- For a base of 6 cm:
[tex]\[
\text{Height} = \frac{36}{6} = 6.0 \, \text{cm}
\][/tex]
- For a base of 10 cm:
[tex]\[
\text{Height} = \frac{36}{10} = 3.6 \, \text{cm}
\][/tex]
- For a base of 36 cm:
[tex]\[
\text{Height} = \frac{36}{36} = 1.0 \, \text{cm}
\][/tex]
Now we have all the heights for the new rectangles with the given bases, ensuring they all have the same area as the original rectangle.
1. Identify the original rectangle's measurements:
- The base (width) of the original rectangle is 18 centimeters.
- The height of the original rectangle is 2 centimeters.
2. Calculate the area of the original rectangle:
- The area of a rectangle can be calculated using the formula:
[tex]\[
\text{Area} = \text{base} \times \text{height}
\][/tex]
- For the original rectangle, the area is:
[tex]\[
\text{Area} = 18 \, \text{cm} \times 2 \, \text{cm} = 36 \, \text{cm}^2
\][/tex]
3. Write down the new base lengths given for the other rectangles:
- The new bases are 5 cm, -1 cm, 6 cm, 10 cm, and 36 cm.
4. Calculate the height for each of the new rectangles:
- Since all new rectangles must have the same area as the original (36 cm²), we can use the formula:
[tex]\[
\text{Height} = \frac{\text{Area}}{\text{base}}
\][/tex]
- Using this formula, calculate each height:
- For a base of 5 cm:
[tex]\[
\text{Height} = \frac{36}{5} = 7.2 \, \text{cm}
\][/tex]
- For a base of -1 cm (usually not practical, just theoretical):
[tex]\[
\text{Height} = \frac{36}{-1} = -36 \, \text{cm}
\][/tex]
- For a base of 6 cm:
[tex]\[
\text{Height} = \frac{36}{6} = 6.0 \, \text{cm}
\][/tex]
- For a base of 10 cm:
[tex]\[
\text{Height} = \frac{36}{10} = 3.6 \, \text{cm}
\][/tex]
- For a base of 36 cm:
[tex]\[
\text{Height} = \frac{36}{36} = 1.0 \, \text{cm}
\][/tex]
Now we have all the heights for the new rectangles with the given bases, ensuring they all have the same area as the original rectangle.
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