Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle.(1 point) No, because 369 is not equal to 100. No, because 369 is not equal to 100. No, because 244 is not equal to 225.No, because 325 is not equal to 144. No, because 325 is not equal to 144. No, because 22 is not equal to 15.
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No, because 325 is not equal to 144.
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According to the converse of the Pythagorean theorem, if the sum of the squares of the two shorter sides of a triangle is equal to the square of the longest side, then the triangle is a right triangle.
In this case, the square of the longest side, 15, is 225 (15^2). The sum of the squares of the two shorter sides, 10 and 12, is 244 (10^2 + 12^2).
Since 225 is not equal to 244, the triangle with sides 15, 10, and 12 is not a right triangle.
According to the converse of the Pythagorean theorem, if the sum of the squares of the two shorter sides of a triangle is equal to the square of the longest side, then the triangle is a right triangle.
In this case, the square of the longest side, 15, is 225 (15^2). The sum of the squares of the two shorter sides, 10 and 12, is 244 (10^2 + 12^2).
Since 225 is not equal to 244, the triangle with sides 15, 10, and 12 is not a right triangle.
Whats the missing leg length of 18^2 + b^2 = 30^2 and is it a right triangle?
To find the length of the missing leg (b) in the equation 18^2 + b^2 = 30^2, we can solve for b.
Simplifying the equation, we have:
324 + b^2 = 900
Subtracting 324 from both sides, we get:
b^2 = 900 - 324
b^2 = 576
Taking the square root of both sides, we find:
b = √576
b = 24
So, the missing leg has a length of 24 units.
To determine if the triangle is a right triangle, we can check if the Pythagorean theorem holds using the given sides. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side.
In this case, we have:
18^2 + 24^2 = 30^2
324 + 576 = 900
The two sides' squares do indeed add up to the square of the longest side (900), so the triangle with side lengths 18, 24, and 30 is a right triangle.
Simplifying the equation, we have:
324 + b^2 = 900
Subtracting 324 from both sides, we get:
b^2 = 900 - 324
b^2 = 576
Taking the square root of both sides, we find:
b = √576
b = 24
So, the missing leg has a length of 24 units.
To determine if the triangle is a right triangle, we can check if the Pythagorean theorem holds using the given sides. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side.
In this case, we have:
18^2 + 24^2 = 30^2
324 + 576 = 900
The two sides' squares do indeed add up to the square of the longest side (900), so the triangle with side lengths 18, 24, and 30 is a right triangle.
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