https://file.aiquickdraw.com/mathbot/file/17269893309149zhp3ejb.jpg

We are given an L-shaped bracket with:

- Overall length \( L = 9.7 \, \text{cm} \),
- Overall width \( W = 2.6 \, \text{cm} \),
- The area of the bracket \( A = 15.7 \, \text{cm}^2 \),
- The unknown \( x \), which represents the small cutout lengths on the L-shape.

### Step-by-step solution:

1. **Break down the area of the L-shaped bracket:**
   The L-shape can be seen as a large rectangle with dimensions \( L \times W \) minus a small rectangular cutout of dimensions \( x \times x \).

   - The area of the large rectangle is \( L \times W = 9.7 \, \text{cm} \times 2.6 \, \text{cm} = 25.22 \, \text{cm}^2 \).
   - The area of the small cutout is \( x^2 \).

2. **Set up the equation for the total area:**
   \[
   \text{Area of the L-shape} = (\text{Area of large rectangle}) - (\text{Area of cutout}) 
   \]
   \[
   15.7 \, \text{cm}^2 = 25.22 \, \text{cm}^2 - x^2
   \]

3. **Solve for \( x \):**
   \[
   x^2 = 25.22 - 15.7 = 9.52
   \]
   \[
   x = \sqrt{9.52} \approx 3.09 \, \text{cm}
   \]

Thus, the value of \( x \) is approximately **3.09 cm**.

Would you like more details on any step?

---

Here are some follow-up questions for further understanding:

1. What other shapes could the L-shaped figure be divided into to make calculations easier?
2. How would you calculate the perimeter of the L-shaped bracket?
3. If the length \( L \) or width \( W \) changed, how would that affect the value of \( x \)?
4. Can the formula for area subtraction be applied to other irregular shapes?
5. What would the area of the L-shaped bracket be if the small cutout was doubled in size?

**Tip:** When dealing with complex shapes, breaking them into simpler shapes like rectangles or triangles can make calculations easier.

The L-shaped bracket shown below has an overall length of L = 9.7 cm and an overall width of W = 2.6 cm. Find x if the area of the bracket is 15.7 cm².

Learn how to find the value of x in an L-shaped bracket with overall length 9.7 cm, width 2.6 cm, and area 15.7 cm². This problem covers algebra and geometry concepts, including the area calculation and solving quadratic equations. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation