College Algebra Midterm Study Guidance – Triangle Sides and the Pythagorean Theorem

Q16. Which of the following equations represent the sides of a triangle given below?

Background

Topic: The Square Root Property / Pythagorean Theorem

This question tests your understanding of how to relate the sides of a right triangle using the Pythagorean Theorem. You need to identify which equation correctly expresses the relationship between the three sides labeled as x, x+9, and 3x-3.

Key Terms and Formulas

• Pythagorean Theorem: For a right triangle with legs a and b, and hypotenuse c:

$a^2 + b^2 = c^2$

• Legs: The two shorter sides of the triangle.

• Hypotenuse: The longest side, opposite the right angle.

Step-by-Step Guidance

1. Examine the triangle and identify which side is likely the hypotenuse (the longest side). Compare the expressions x, x+9, and 3x-3 for possible values of x.

2. Recall that the Pythagorean Theorem relates the two legs and the hypotenuse: $a^2 + b^2 = c^2$.

3. Assign the sides to the variables a, b, and c based on their likely roles (legs or hypotenuse).

4. Set up the equation using the expressions for the sides. For example, if x and x+9 are the legs and 3x-3 is the hypotenuse, the equation would be $x^2 + (x+9)^2 = (3x-3)^2$.

5. Expand and simplify the equation to check if it matches any of the answer choices.

Try solving on your own before revealing the answer!

Final Answer: x^2 + (x+9)^2 = (3x-3)^2

This equation uses the Pythagorean Theorem, with x and x+9 as the legs and 3x-3 as the hypotenuse.