Math Problem Statement

Find the length of x in a right triangle, where AB = 10.5, BC = 9, and DE = 3.5.

Solution

The problem in the image is asking to find the length of xx in a right triangle. Given the dimensions, we can solve this using the Pythagorean theorem.

Problem Recap:

  • Triangle ABC\triangle ABC is a right triangle.
  • The length of side AB=10.5AB = 10.5.
  • The length of side AC=xAC = x.
  • The length of side BC=9BC = 9.
  • The length of side DE=3.5DE = 3.5.

Approach:

To find xx, we can apply the Pythagorean theorem, which states:

AB2=AC2+BC2AB^2 = AC^2 + BC^2

Substituting the given values:

10.52=x2+9210.5^2 = x^2 + 9^2

Solve for xx:

  1. Calculate the squares of the given numbers: 10.52=110.2510.5^2 = 110.25 92=819^2 = 81

  2. Substitute these into the equation: 110.25=x2+81110.25 = x^2 + 81

  3. Solve for x2x^2: x2=110.2581x^2 = 110.25 - 81 x2=29.25x^2 = 29.25

  4. Take the square root of both sides: x=29.255.41x = \sqrt{29.25} \approx 5.41

So, the length of xx is approximately 5.415.41 units.


Do you want further details or have any questions? Here are 5 related questions you might find helpful:

  1. How does the Pythagorean theorem apply to different types of triangles?
  2. Can you explain how to calculate the square root without a calculator?
  3. What are the implications if the triangle isn't a right triangle?
  4. How would the problem change if you were given the hypotenuse and one leg?
  5. What are some real-world applications of the Pythagorean theorem?

Tip: Always double-check your work by verifying the calculation steps, especially when working with squared numbers and square roots.

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangles
Pythagorean Theorem

Formulas

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

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 8-10