Sure, let's solve the problem step by step.
You are given the dimensions of a rectangle: a width of 3 cm and a height of 7 cm. Additionally, you are provided with a total area of 24 square centimeters, and you need to determine the missing side [tex]\( x \)[/tex] of a rectangle when one of the sides is already given.
### Step-by-Step Solution:
1. Understand the given dimensions:
- Width of the rectangle [tex]\( w \)[/tex] = 3 cm
- Height of the rectangle [tex]\( h \)[/tex] = 7 cm
- Given area [tex]\( A \)[/tex] = 24 cm²
2. Calculate the area using width and height:
- The area of a rectangle is calculated by multiplying the width by the height.
- [tex]\( \text{Calculated Area} = w \times h = 3 \, \text{cm} \times 7 \, \text{cm} = 21 \, \text{cm}² \)[/tex]
3. Compare the calculated area with the given area:
- The calculated area of the rectangle using the given dimensions (21 cm²) does not match the given area (24 cm²).
4. Identify the problem:
- Since the calculated area is not equal to the given area, there must be an error in the dimensions or we need to find different dimensions that match the given area.
5. Resolve the error by finding the missing side [tex]\( x \)[/tex]:
- Let's assume the actual width remains 3 cm, and we need to find the missing length [tex]\( x \)[/tex] that will give us an area of 24 cm².
- Using the formula for the area of a rectangle again:
[tex]\[ \text{Area} (A) = \text{width} \times \text{length} \quad \Rightarrow \quad x = \frac{A}{\text{width}} \][/tex]
- Substitute the given values:
[tex]\[ x = \frac{24 \, \text{cm}²}{3 \, \text{cm}} = 8 \, \text{cm} \][/tex]
### Conclusion:
So, we conclude that if the width is 3 cm and we require the area to be 24 cm², the other side [tex]\( x \)[/tex] must be 8 cm.
