The area of a square is 49h² - 154h + 121 square units. What is the length of each side?

To find the length of each side of a square, we take the square root of the area of the square. 

The given area of the square is \( 49h^2 - 154h + 121 \). 

So, we need to factor this quadratic expression as a perfect square trinomial:

1. The expression \( 49h^2 - 154h + 121 \) can be factored as:
   \[
   (7h - 11)^2
   \]

2. Therefore, the length of each side of the square is the square root of \( 49h^2 - 154h + 121 \), which is \( 7h - 11 \).

### Answer: 
The length of each side of the square is \( 7h - 11 \) units.

Would you like more details or have any questions?

### Related Questions:
1. How do you factor perfect square trinomials?
2. What are the steps for completing the square for a quadratic expression?
3. How can you find the perimeter of the square if the side length is \( 7h - 11 \)?
4. What happens if the quadratic expression doesn't factor into a perfect square?
5. How do you derive the quadratic formula from the standard form of a quadratic equation?
6. Can you generalize the method for finding the side of a square if the area is any quadratic expression?
7. What are some real-life applications of perfect square trinomials?
8. How would the problem change if the area of the square were given as a cubic expression?

#### Tip: 
Always check if a quadratic expression is a perfect square trinomial by comparing it with \( (ax + b)^2 = a^2x^2 + 2abx + b^2 \).

Learn how to find the length of each side of a square when the area is given as 49h² - 154h + 121. This problem involves factoring a perfect square trinomial and applying square root principles. Suitable for advanced high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation