Questions: Determinar la medida de x A) 12 cm B) 10 cm C) 14 cm D) 15 cm

Transcript text: 22. Determinar la medida de $x$ A) 12 cm B) 10 cm C) 14 cm D) 15 cm

Solution

Solution Steps

Step 1: Identify the type of triangle

The given triangle is a right-angled triangle with sides of 6 cm and 8 cm, and the hypotenuse is $ x $ cm.

Step 2: Apply the Pythagorean Theorem

The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse ($ x $) is equal to the sum of the squares of the other two sides. \[ x^2 = 6^2 + 8^2 \]

Step 3: Calculate the squares of the sides

Calculate the squares of 6 and 8: \[ 6^2 = 36 \] \[ 8^2 = 64 \]

Step 4: Sum the squares

Add the squares of the two sides: \[ 36 + 64 = 100 \]

Step 5: Solve for $ x $

Take the square root of the sum to find $ x $: \[ x = \sqrt{100} = 10 \]

Final Answer

The measure of $ x $ is $ 10 $ cm.

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