The correct answer is D. No, because 22 is not equal to 15.
According to the converse of the Pythagorean theorem, if the square of the length of the longest side of a triangle is not equal to the sum of the squares of the other two sides, then the triangle is not a right triangle.
In this case, using the converse of the Pythagorean theorem, we calculate that 15^2 + 10^2 = 225 + 100 = 325, which is not equal to the square of the length of the longest side, 12^2 = 144. Therefore, the triangle with sides 15, 10, and 12 is not a right triangle.
Using the converse of the Pythagorean theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle.
A. No, because 244 is not equal to 225
B. No, because 369 is not equal to 100
C. No, because 325 is not equal to 144
D. No, because 22 is not equal to 15
3 answers
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The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse). Mathematically, it can be written as:
a^2 + b^2 = c^2
where a and b are the lengths of the legs, and c is the length of the hypotenuse.
Now, the converse of the Pythagorean theorem states that if in a triangle, the sum of the squares of the lengths of two sides is equal to the square of the length of the third side, then the triangle is a right triangle.
In this case, we have a triangle with sides 15, 10, and 12. To determine if it is a right triangle, we need to check if the sum of the squares of the two shorter sides (15 and 10) is equal to the square of the longest side (12).
Using the Pythagorean theorem, we find that 15^2 + 10^2 = 225 + 100 = 325. However, this is not equal to the square of the longest side (12^2 = 144).
Since the sum of the squares of the two shorter sides is not equal to the square of the longest side, we can conclude that the triangle with sides 15, 10, and 12 is not a right triangle, according to the converse of the Pythagorean theorem.
Therefore, the correct answer is D. No, because 22 is not equal to 15.
The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse). Mathematically, it can be written as:
a^2 + b^2 = c^2
where a and b are the lengths of the legs, and c is the length of the hypotenuse.
Now, the converse of the Pythagorean theorem states that if in a triangle, the sum of the squares of the lengths of two sides is equal to the square of the length of the third side, then the triangle is a right triangle.
In this case, we have a triangle with sides 15, 10, and 12. To determine if it is a right triangle, we need to check if the sum of the squares of the two shorter sides (15 and 10) is equal to the square of the longest side (12).
Using the Pythagorean theorem, we find that 15^2 + 10^2 = 225 + 100 = 325. However, this is not equal to the square of the longest side (12^2 = 144).
Since the sum of the squares of the two shorter sides is not equal to the square of the longest side, we can conclude that the triangle with sides 15, 10, and 12 is not a right triangle, according to the converse of the Pythagorean theorem.
Therefore, the correct answer is D. No, because 22 is not equal to 15.
5 answers