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Transcript text: Extension

Solution

Solution Steps

Step 1: Identify the type of triangle

The given triangle has sides of 8 meters, 13 meters, and an unknown side \( w \). This is a right triangle because the sides follow the Pythagorean theorem.

Step 2: Apply the Pythagorean theorem

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Here, 13 meters is the hypotenuse.

\[ 13^2 = 8^2 + w^2 \]

Step 3: Solve for \( w \)

Calculate the squares of the known sides:

\[ 13^2 = 169 \] \[ 8^2 = 64 \]

Substitute these values into the equation:

\[ 169 = 64 + w^2 \]

Subtract 64 from both sides to isolate \( w^2 \):

\[ w^2 = 169 - 64 \] \[ w^2 = 105 \]

Take the square root of both sides to find \( w \):

\[ w = \sqrt{105} \] \[ w \approx 10.25 \, \text{meters} \]