What type of triangle has side lengths 7, 24, and 25?Group of answer choicesright triangleisosceles trianglenot a triangleobtuse triangleacute triangle
Question
What type of triangle has side lengths 7, 24, and 25?
Group of answer choices
- right triangle
- isosceles triangle
- not a triangle
- obtuse triangle
- acute triangle
Solution
This is a right triangle. We can determine this by using the Pythagorean theorem, which states that 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.
If we square each of the given side lengths, we get 49 (7^2), 576 (24^2), and 625 (25^2).
Adding the squares of the two smaller side lengths gives us 49 + 576 = 625, which is equal to the square of the largest side length.
Therefore, the triangle with side lengths 7, 24, and 25 is a right triangle.
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