pq 6x 25 and qr 16 3x find pr

Guri Bee

2 min read

·

23-10-2024

1

0

Share

Finding the Missing Side: A Step-by-Step Guide to Solving for PR

This article will guide you through the process of finding the length of side PR in a triangle, given the lengths of two other sides and an additional piece of information. We will use the concept of Pythagorean Theorem to solve this problem.

The Problem:

We are given a triangle where:

• PQ = 6x + 25
• QR = 16 + 3x

We need to find the length of PR.

Understanding the Problem:

The given information suggests that we have a right triangle. This is because we are provided with the lengths of two sides and need to find the third. This scenario is perfect for applying the Pythagorean Theorem.

The Pythagorean Theorem:

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In mathematical terms:

a² + b² = c²

where:

• a and b are the lengths of the two shorter sides (legs)
• c is the length of the hypotenuse.

Applying the Theorem:

1. Identify the Hypotenuse: We need to determine which side is the hypotenuse. The problem doesn't explicitly state it, but it's likely that PR is the hypotenuse, given its position.

2. Substitute the Values: Let's assume PR is the hypotenuse. We can then write:

   (6x + 25)² + (16 + 3x)² = PR²
   

3. Simplify the Equation: Expanding the squares and combining like terms:

   36x² + 300x + 625 + 9x² + 96x + 256 = PR²
   

   Simplifying further:

   45x² + 396x + 881 = PR²
   

4. Solve for PR: To find PR, we need to take the square root of both sides of the equation. However, we need more information to solve for x.

Additional Information Needed:

To solve for PR, we need additional information about the triangle. This information could be:

• The length of one of the sides (PQ or QR)
• The value of x
• The measure of one of the angles

Example Scenario:

Let's assume we are given that PQ = 50. We can then use this information to solve for x:

6x + 25 = 50
6x = 25
x = 25/6

Now we can substitute the value of x back into the equation for PR²:

PR² = 45 (25/6)² + 396 (25/6) + 881

Solving for PR gives us:

PR ≈ 63.8

Conclusion:

Finding the missing side of a right triangle involves applying the Pythagorean Theorem and utilizing the information provided about the triangle's sides or angles. Remember to carefully identify the hypotenuse and substitute the given values into the theorem.