Math Problem Statement

Solve for x

Solve for x

Solution

Let's break down the image to solve for xx.

We have a right triangle ABC\triangle ABC where:

  • C=90\angle C = 90^\circ
  • The length of side BC=12cmBC = 12 \, \text{cm}
  • There is another right triangle BED\triangle BED, and BED=90\angle BED = 90^\circ.
  • BE=8cmBE = 8 \, \text{cm}, ED=6cmED = 6 \, \text{cm}

We are tasked with finding xx, the length of ABAB.

Step 1: Apply the Pythagorean theorem to triangle ABCABC:

In right triangle ABCABC, we know that:

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

Step 2: Use the known values:

  • BC=12cmBC = 12 \, \text{cm}
  • AC=8cmAC = 8 \, \text{cm} (from the given dimensions in the image)

Substitute these into the Pythagorean theorem:

AB2=82+122=64+144=208AB^2 = 8^2 + 12^2 = 64 + 144 = 208

AB=208=413cmAB = \sqrt{208} = 4\sqrt{13} \, \text{cm}

So, the value of xx (which is ABAB) is 413cm4\sqrt{13} \, \text{cm}, or approximately 11.44cm11.44 \, \text{cm}.

Would you like a more detailed explanation or further assistance with any other questions?

Here are some related questions:

  1. How do you solve a right triangle using the Pythagorean theorem?
  2. What is the difference between the hypotenuse and legs in a right triangle?
  3. How do you use the Pythagorean theorem in three-dimensional problems?
  4. What is the formula for the area of a right triangle?
  5. How do you apply trigonometric ratios in right triangles?

Tip: Always double-check the units you are using in problems, especially in geometry, to ensure consistency and avoid errors in your calculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangles
Pythagorean Theorem

Formulas

AB^2 = AC^2 + BC^2

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 8-10