Which of the following triangles is a right triangle given the measure of the sides.*A. 1 unit, 2 units, 3 unitsB. 4 units, 5 units, 10 unitsC. 3 units, 4 units, 5 unitsD. 6 units, 7 units, 12 units
Question
Which of the following triangles is a right triangle given the measure of the sides.*A. 1 unit, 2 units, 3 unitsB. 4 units, 5 units, 10 unitsC. 3 units, 4 units, 5 unitsD. 6 units, 7 units, 12 units
Solution
The answer is C. 3 units, 4 units, 5 units. This is because in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This is known as the Pythagorean theorem.
For option C, if you square the lengths of the sides, you get 9, 16, and 25. The sum of 9 and 16 is 25, which is the square of the length of the hypotenuse. Therefore, this is a right triangle.
For the other options, the sum of the squares of the lengths of the two shorter sides is not equal to the square of the length of the longest side, so they are not right triangles.
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