Question
What length is needed to make a right triangle with the sides 9 and 15, with 15 being the longest?
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GPT 3.5
The length needed to make a right triangle with sides 9 and 15, with 15 being the longest side, can be found using the Pythagorean theorem.
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, it can be written as:
c^2 = a^2 + b^2
where:
c = length of the hypotenuse (15 in this case)
a = length of one of the other sides (9 in this case)
b = length of the other side (the unknown side)
Substitute the given values into the equation:
15^2 = 9^2 + b^2
225 = 81 + b^2
b^2 = 225 - 81
b^2 = 144
Taking the square root of both sides gives:
b = √144
b = 12
Therefore, the length needed to make a right triangle with sides 9 and 15, with 15 being the longest, is 12 units.
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, it can be written as:
c^2 = a^2 + b^2
where:
c = length of the hypotenuse (15 in this case)
a = length of one of the other sides (9 in this case)
b = length of the other side (the unknown side)
Substitute the given values into the equation:
15^2 = 9^2 + b^2
225 = 81 + b^2
b^2 = 225 - 81
b^2 = 144
Taking the square root of both sides gives:
b = √144
b = 12
Therefore, the length needed to make a right triangle with sides 9 and 15, with 15 being the longest, is 12 units.
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