https://file.aiquickdraw.com/mathbot/file/1725596036210deafye8z.jpg

The problem in the image appears to describe a situation involving a right triangle and the Pythagorean theorem. Here's a summary of the text:

A person has enough garden soil to make a garden bed with an area of 6 square yards. The garden bed is shaped like a right triangle. One leg of the right triangle is 3 yards long, and you are asked to determine the length of the other leg.

### Step-by-Step Solution:

1. **Area Formula for a Right Triangle**:  
   The area \( A \) of a right triangle is given by the formula:
   \[
   A = \frac{1}{2} \times \text{base} \times \text{height}
   \]
   In this problem, the area is provided as 6 square yards, and one of the legs (base or height) is 3 yards.

2. **Setting up the equation**:
   \[
   6 = \frac{1}{2} \times 3 \times h
   \]
   where \( h \) is the unknown leg (height).

3. **Solving for \( h \)**:
   Multiply both sides of the equation by 2 to eliminate the fraction:
   \[
   12 = 3 \times h
   \]
   Now, divide by 3:
   \[
   h = \frac{12}{3} = 4 \, \text{yards}
   \]

### Final Answer:
The length of the other leg of the right triangle is **4 yards**.

Would you like more details or have any questions?

Here are five related questions to expand the topic:
1. How would the solution change if the area was doubled but one leg remained the same?
2. Can the Pythagorean theorem be used in this problem to confirm the leg lengths?
3. What is the hypotenuse of this right triangle, based on the two legs?
4. How do you calculate the perimeter of this triangular garden bed?
5. If the garden bed was not a right triangle, how would you approach finding the other side?

**Tip:** Always check if the dimensions provided correspond to a right triangle to apply the Pythagorean theorem if needed.

Tara has enough garden soil to make a garden bed with an area of 6 square yards. She wants to build the garden bed in the corner of her yard in the shape of a right triangle. Because of the location of her garden, one leg of the triangle must be 3 yards long. Determine the length of the other leg of the triangle.

Solve a right triangle garden bed problem by finding the length of the unknown leg using the area formula. Given that one leg is 3 yards and the area is 6 square yards, this step-by-step solution 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