Math Problem Statement

Find the value of x in the triangle shown below.

Solution

To find the value of xx in the right triangle shown, we can use the Pythagorean theorem:

a2+b2=c2a^2 + b^2 = c^2

where cc is the hypotenuse, and aa and bb are the two legs of the right triangle.

Here:

  • a=9a = 9
  • b=xb = x (the unknown side we need to solve for)
  • c=15c = 15 (the hypotenuse)

Applying the Pythagorean theorem:

92+x2=1529^2 + x^2 = 15^2

Calculating each term:

  1. 92=819^2 = 81
  2. 152=22515^2 = 225

Now substitute these values:

81+x2=22581 + x^2 = 225

Subtract 81 from both sides:

x2=22581x^2 = 225 - 81

x2=144x^2 = 144

Take the square root of both sides:

x=144x = \sqrt{144}

x=12x = 12

So, the correct answer is:

(B) x=12x = 12

Would you like further details on this solution, or have any additional questions?

Here are 5 related questions that can help deepen your understanding:

  1. How can the Pythagorean theorem be applied to other types of triangles?
  2. What happens if all sides of a triangle are known? Can we still use the Pythagorean theorem?
  3. How does one determine if a triangle is a right triangle using only side lengths?
  4. If one side of a right triangle is doubled, how does that affect the hypotenuse?
  5. Can the Pythagorean theorem be used in three-dimensional space?

Tip: Always verify which side is the hypotenuse in a right triangle when applying the Pythagorean theorem.

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangle
Pythagorean Theorem

Formulas

a^2 + b^2 = c^2

Theorems

Pythagorean Theorem

Suitable Grade Level

Grade 8-10