Questions: If the base of a rectangle is 83 / 5 cm and the area is 473 / 10 cm^2, what is the height of the rectangle?

If the base of a rectangle is 83 / 5 cm and the area is 473 / 10 cm^2, what is the height of the rectangle?
Transcript text: 2. If the base of a rectangle is $83 / 5 \mathrm{~cm}$ and the area is $473 / 10 \mathrm{~cm}^{2}$, what is the height of the rectangle?
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Solution

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Solution Steps

To find the height of the rectangle, we can use the formula for the area of a rectangle, which is given by:

\[ \text{Area} = \text{Base} \times \text{Height} \]

We can rearrange this formula to solve for the height:

\[ \text{Height} = \frac{\text{Area}}{\text{Base}} \]

Given the base and the area, we can substitute these values into the formula to find the height.

Step 1: Given Values

We are given the base and the area of a rectangle:

  • Base: \( \frac{83}{5} \) cm
  • Area: \( \frac{473}{10} \) cm\(^2\)
Step 2: Convert to Decimal Form

Convert the given fractions to decimal form:

  • Base: \( \frac{83}{5} = 16.6 \) cm
  • Area: \( \frac{473}{10} = 47.3 \) cm\(^2\)
Step 3: Use the Area Formula

The formula for the area of a rectangle is: \[ \text{Area} = \text{Base} \times \text{Height} \]

Rearrange the formula to solve for the height: \[ \text{Height} = \frac{\text{Area}}{\text{Base}} \]

Step 4: Calculate the Height

Substitute the given values into the formula: \[ \text{Height} = \frac{47.3}{16.6} \approx 2.849 \]

Final Answer

The height of the rectangle is: \[ \boxed{2.849 \text{ cm}} \]

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