Questions: If the line segment AD is 10 inches long and the line segment BD is 6 inches long, find the length of the line segment AB.

If the line segment AD is 10 inches long and the line segment BD is 6 inches long, find the length of the line segment AB.
Transcript text: If $\overline{A D}$ is $\mathbf{1 0}$ inches long. $\overline{B D}$ is $\mathbf{6}$ inches long. 1. Find the length of $\overline{A B}$.
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Solution

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Solution Steps

Step 1: Identify the given information

We are given that AD = 10 inches and BD = 6 inches. We also see that triangle ADB is a right triangle with a right angle at B.

Step 2: Apply the Pythagorean theorem

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 triangle ADB, AD is the hypotenuse, so we have:

AB² + BD² = AD²

Step 3: Substitute the known values

We know AD = 10 and BD = 6, so we can substitute these values into the equation:

AB² + 6² = 10²

Step 4: Simplify and solve for AB

AB² + 36 = 100 AB² = 100 - 36 AB² = 64 AB = √64 AB = 8

Final Answer

The length of AB is 8 inches.

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