https://file.aiquickdraw.com/mathbot/file/1726241001805ucodudkx.jpg

The problem involves a right triangle where one leg is given as 12 ft, and the area of the shaded region is 108 ft². We are asked to find the missing length \( v \), which is the other leg of the triangle.

### Key Information:
- The formula for the area of a right triangle is:
  \[
  \text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
  \]
  Here, the base is 12 ft, and the height is \( v \).

- The area is given as 108 ft².

### Solving for \( v \):
We use the area formula and solve for \( v \):
\[
108 = \frac{1}{2} \times 12 \times v
\]
Multiplying both sides by 2 to eliminate the fraction:
\[
216 = 12 \times v
\]
Now, divide by 12 to isolate \( v \):
\[
v = \frac{216}{12} = 18 \, \text{ft}
\]

Thus, the missing length \( v \) is 18 feet.

Would you like further details or have any other questions?

---

Here are some related questions:
1. How would the formula change if it were a non-right triangle?
2. How can you verify the accuracy of your answer using the Pythagorean Theorem?
3. What would happen if the area of the triangle changed to 150 ft²? How would \( v \) change?
4. Can you apply this formula to any triangle or only specific types?
5. What if you were given the hypotenuse instead? How would you find the legs?

**Tip:** Always remember to double-check your units when solving problems involving area, as unit conversions can sometimes cause confusion.

What is the missing length in the right triangle where the base is 12 ft and the area of the shaded region is 108 ft²?

Learn how to find the missing length of a right triangle with a base of 12 feet and a given area of 108 square feet. This problem uses the area formula for right triangles and is suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation