In triangle DEF, if angle D is 90 degrees and the lengths of the legs are 6 cm a

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Question: In triangle DEF, if angle D is 90 degrees and the lengths of the legs are 6 cm and 8 cm, what is the length of the hypotenuse?

Options:

Correct Answer: 10 cm

Solution:

Using the Pythagorean theorem, hypotenuse = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.

In triangle DEF, if angle D is 90 degrees and the lengths of the legs are 6 cm and 8 cm, what is the length of the hypotenuse?

In triangle DEF, if angle D is 90 degrees and the lengths of the legs are 6 cm and 8 cm, what is the length of the hypotenuse?

Step 1: Identify that triangle DEF is a right triangle because angle D is 90 degrees.
Step 2: Recognize that the lengths of the legs of the triangle are 6 cm and 8 cm.
Step 3: Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). This can be written as: c² = a² + b².
Step 4: Substitute the lengths of the legs into the formula. Here, a = 6 cm and b = 8 cm, so we have: c² = 6² + 8².
Step 5: Calculate 6², which is 36, and 8², which is 64.
Step 6: Add the results from Step 5: 36 + 64 = 100.
Step 7: Take the square root of 100 to find the length of the hypotenuse: √100 = 10 cm.

Pythagorean Theorem – A mathematical principle used to find the length of a side in a right triangle, stating that the square of the hypotenuse is equal to the sum of the squares of the other two sides.