Math Problem Statement

Find the value of x in the triangle with sides 9, 15, and x.

Solution

Let's solve the problem using the Pythagorean theorem.

The triangle in the image is a right triangle, where:

  • Hypotenuse c=15c = 15,
  • One leg a=9a = 9,
  • The other leg b=xb = x (which we need to find).

The Pythagorean theorem states: a2+b2=c2a^2 + b^2 = c^2 Substitute the known values: 92+x2=1529^2 + x^2 = 15^2 81+x2=22581 + x^2 = 225 Now, isolate x2x^2: x2=22581=144x^2 = 225 - 81 = 144 Take the square root of both sides: x=144=12x = \sqrt{144} = 12

So, the correct answer is: Cx=12\boxed{C} \quad x = 12

Let me know if you have any questions or need further clarification!


Here are 5 follow-up questions to explore the topic further:

  1. How does the Pythagorean theorem apply to 3D shapes like pyramids or cubes?
  2. Can the Pythagorean theorem be used for non-right triangles?
  3. How do you determine which side is the hypotenuse in any right triangle?
  4. What happens if one of the triangle’s sides is given as a square root value?
  5. Can the Pythagorean theorem help in real-world problems, such as navigation?

Tip: Always verify which side is the hypotenuse in a right triangle—it’s the longest side and always opposite the right angle.

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangles

Formulas

Pythagorean theorem: a^2 + b^2 = c^2

Theorems

Pythagorean theorem

Suitable Grade Level

Grades 7-9